%%manim -qm -v WARNING senoide_estatica1
class senoide_estatica1(Scene):
def construct(self):
##############################################################################
# CRIAR OBJETOS MANIM
##############################################################################
Ac1 = ValueTracker(1) # rastreador da amplitude c1
w1 = ValueTracker(1)
phic1 = ValueTracker(0)
Ac2 = ValueTracker(1) # rastreador da amplitude c2
w2 = ValueTracker(1)
phic2 = ValueTracker(0)
n1 = MathTex('f(t) = A sin(\omega t +\\phi)').move_to([-3,1.5,0]).set_color_by_gradient([RED, WHITE]).scale(1.2)
n2 = MathTex('g(t) = A cos(\omega t +\\phi)').move_to([3.5,1.5,0]).set_color_by_gradient([RED, WHITE]).scale(1.2)
n3 = Tex('\\textit{Senoides}', color = YELLOW).move_to([-3,-0.5,0]).scale(1.5)
n4 = Tex('\\textit{Cossenoides}', color = YELLOW).move_to([3.5,-0.5,0]).scale(1.5)
n5 = Tex('\\textsc{Domínio do tempo}', opacity = 1).move_to([0,-2.5,0]).set_color_by_gradient([GRAY, WHITE])
ne4 = MathTex('F( \\theta)=sin( \\theta)').move_to([-3,1.5,0]).scale(1.2).set_color_by_gradient([BLUE, WHITE])
n6 = MathTex('G( \\theta)=cos( \\theta)').move_to([3,1.5,0]).scale(1.2).set_color_by_gradient([BLUE, WHITE])
n7 = Tex('\\textsc{Domínio do Ângulo}').move_to([0,-1,0]).set_color_by_gradient([GRAY, WHITE])
n8 = Tex('\\textit{Mudar Domínio}').move_to([0,-2,0]).scale(1.5)
n9 = MathTex('G(t)=cos(t)').move_to([0,0,0]).set_color_by_gradient([YELLOW, WHITE]).scale(1.2)
def f1(x):
return Ac1.get_value()*np.cos(x)
def f2(x):
return Ac2.get_value()*np.cos(x)
E1 = Axes(x_range = [-9,9,2], y_range = [-2,3,1] , x_length = 4, y_length = 3).move_to([-3.5,0,0])
n10 = always_redraw(lambda: MathTex('y').next_to( E1, UP, buff = 0 ).shift(0.3*LEFT) )
n11 = always_redraw(lambda: MathTex('\\theta').next_to( E1, RIGHT, buff = 0).shift(0.3*DOWN) )
c1 = E1.plot(lambda x: f1(x), x_range = [-7,7], color = YELLOW)
E2 = Axes(x_range = [-9,9,2], y_range = [-2,3,1] , x_length = 4, y_length = 3).move_to([3.5,0,0])
n12 = always_redraw(lambda: MathTex('y').next_to( E2, UP, buff = 0 ).shift(0.3*LEFT) )
n13 = always_redraw(lambda: MathTex('t').next_to( E2, RIGHT, buff = 0).shift(0.3*DOWN) )
c2 = E2.plot(lambda x: f2(x), x_range = [-7,7], color = YELLOW)
G0 = VGroup(E1,n10,n11,n6, c1)
G1 = VGroup(E2, n12,n9,n13, c2)
ne = Text('A - Amplitude').move_to([0,3,0])
######################################################### Equação envolvendo amplitude
ne01 = MathTex('A \\cdot G(t)=').move_to([3.4,1.5,0])
ne02 = MathTex('cos(t)').next_to(ne01, RIGHT, buff = 0.7)
ne1 = VGroup(ne01,ne02)
#########################################################
# CRIAR OBJETO n14. OBJETO QUE SIMULA UMA CONTAGEM NUMÉRICA NA TELA.
######################################################### Plano que cobre a cena
def cobrir_cena(x):
retangulo = Rectangle().scale(2).set_opacity(0.7).set_color(BLACK)
if x ==1:
return self.play(FadeIn(retangulo))
if x ==0:
return self.play(FadeOut(retangulo))
#################################################################################
# n14 criar contador numérico
n14 = DecimalNumber(1)
n14.add_updater(lambda d: d.set_value(Ac2.get_value()))
n15 = MathTex('-1\leqslant cos(t)\leqslant 1').move_to([0,0,0]).scale(2).set_color_by_gradient([WHITE,GREEN_E])
n16 = MathTex('-A\leqslant A\cdot cos(t)\leqslant A').move_to([0,0,0]).scale(2).set_color_by_gradient([WHITE,GREEN_E])
# n17 criar contador numérico
n17 = DecimalNumber(1)
n17.add_updater(lambda d: d.set_value(w2.get_value()))
n18_0 = MathTex('G(\\omega \\cdot t)=cos(').move_to([3.8,1.8,0])
n18_1 = MathTex('t)').next_to(n18_0, RIGHT, buff = 0.6)
n18 = VGroup(n18_0, n18_1)
n19_0 = MathTex('\\omega').move_to([-3,3,0]).scale(2)
n19_1 = Text(' - Velocidade Angular').next_to(n19_0, RIGHT, buff = 0.2)
n19 = VGroup(n19_0,n19_1)
caux1=E1.plot(lambda x: f1(x), x_range = [0,2*PI], color = GREEN, stroke_width = 10 )
caux2=E2.plot(lambda x: f2(x), x_range = [0,(2*PI)/w2.get_value()], color = GREEN, stroke_width = 10)
n22 = MathTex('G(\\theta) = G(\\omega \\cdot t)').move_to([0,0,0])
n23 = MathTex('\\theta =\\omega \\cdot t').move_to([0,0,0])
n24 = MathTex('\\omega').move_to([-0.5,0,0])
n25 = MathTex('=').next_to(n24, RIGHT, buff = 0.2)
n26 = MathTex('\\frac{\\theta}{t}').next_to(n25, RIGHT, buff = 0.2)
n28 = MathTex('\\frac{\\bigtriangleup \\theta }{\\bigtriangleup t }').move_to(n26.get_center()+0.2*RIGHT)
n30 = MathTex('T')
n31 = MathTex('\\frac{2 \\pi}{\\bigtriangleup t}')
n32 = MathTex('\\frac{2 \\pi}{\\bigtriangleup t}')
n33 = MathTex('T = \\frac{2 \\pi}{\\omega}')
G02 = VGroup(n24,n25,n28)
G2 = VGroup(n24,n25,n32)
n34_0 = MathTex('f').scale(2)
n34_1 = Text(' - Frequência Angular ').next_to(n34_0, RIGHT, buff = 0.2)
n34 = VGroup(n34_0, n34_1)
n35_0 = Text('N° de ciclos que')
n35_1 = Text('ocorrem em 1 segundo ').next_to(n34_0, DOWN, buff = 0.2)
n35 = VGroup(n35_0, n35_1)
n36 = MathTex('f = \\frac{1}{T}')
n37 = MathTex('T = \\frac{2 \\pi}{\\omega}')
n38 = MathTex('f = \\frac{\\omega}{2 \\pi}')
n39 = MathTex('\\omega = 2 \\pi f')
ne3_0 = MathTex('\\phi').scale(2)
ne3_1 = Text(' - Ângulo de Fase ').next_to(n34_0, RIGHT, buff = 0.2)
ne3= VGroup(ne3_0, ne3_1)
n40_0 = MathTex('G(\\theta + \\phi) = cos(\\theta ')
n40_1 = MathTex(' )').next_to(n40_0, RIGHT, buff = 0.6)
n40 = VGroup(n40_0, n40_1)
# criar n41 contador
n41 = DecimalNumber(0)
n41.add_updater(lambda d: d.set_value(w1.get_value()))
n42_0 = MathTex('G(t +\\phi) = cos(t ')
n42_1 = MathTex(' )').next_to(n42_0, RIGHT, buff = 0.6)
n42 = VGroup(n42_0, n42_1)
# criar n43 contador
n43 = DecimalNumber(0)
n43.add_updater(lambda d: d.set_value(w1.get_value()))
n44 = MathTex('\\phi')
n45 = MathTex('\\phi')
n46 = MathTex('\\phi')
n47 = MathTex('\\phi')
# criar v2 v3 v4 v5
v1_0 = Arrow([0,0,0],[-1,0,0], buff=0)
v1_1 = Arrow([0,0,0],[1,0,0], buff=0)
v1 = VGroup(v1_0, v1_1)
v2 = Arrow(E1.c2p(-0.1,-1.5,0),E1.c2p(-3,-1.5,0), buff=0)
v3 = Arrow(E1.c2p(0.1,-1.5,0),E1.c2p(3,-1.5,0), buff=0)
v4 = Arrow(E2.c2p(-0.1,-1.5,0),E2.c2p(-3,-1.5,0), buff=0)
v5 = Arrow(E2.c2p(0.1,-1.5,0),E2.c2p(3,-1.5,0), buff=0)
n48 = MathTex('G(\\omega t +\\phi) = cos(\\omega t + \\phi) ')
n51 = MathTex('A \\cdot cos(\\omega t + \\phi) ')
n52 = MathTex('g(t)=A \\cdot cos(\\omega \\cdot t + \\phi) ')
L1 = E2.get_vertical_line(E2.i2gp(2*PI, c2 ), color=YELLOW)
####################################################################################################
# PRODUÇÃO CENAS DINÂMICAS
####################################################################################################
text0 = Tex('\\textsc{POWER VISUALS}').shift(UP).set_width(8).set_color_by_gradient(YELLOW, BLUE)
text00 = Tex('\\textit{ Apresenta}').shift(DOWN).set_width(3)
self.wait()
self.play(Write(text0))
self.wait(0.5)
self.play(Write(text00))
self.play(Unwrite(text0), run_time = 0.5)
self.play(Unwrite(text00),run_time = 0.5)
g1 = VGroup(n1, n2)
self.play(Write(g1))
g2 = VGroup(n3, n4)
self.play(Write(g2))
self.wait(7)
self.play(Write(n5)) #ok
self.wait(4)
self.wait(7)
g3 = VGroup(n1,n2,n3,n4,n5)
self.play(FadeOut(g3))
g4 = VGroup(ne4,n6)
self.play(Write(g4), run_time = 2)
self.wait(2)
self.play(Write(n7))
self.wait(2)
self.play(Unwrite(n7))
self.play(FadeOut(ne4), run_time = 2)
self.wait(1.5)
self.play(n6.animate.move_to([0,0,0]), run_time = 2)
self.wait(13)
self.play(Write(n8))
self.wait()
self.play(ReplacementTransform(n6, n9), run_time = 2)
self.wait()
g5 = VGroup(n8,n9)
self.play(FadeOut(g5))
%%manim -qm -v WARNING senoide_estatica2
class senoide_estatica2(Scene):
def construct(self):
##############################################################################
# CRIAR OBJETOS MANIM
##############################################################################
Ac1 = ValueTracker(1) # rastreador da amplitude c1
w1 = ValueTracker(1)
phic1 = ValueTracker(0)
Ac2 = ValueTracker(1) # rastreador da amplitude c2
w2 = ValueTracker(1)
phic2 = ValueTracker(0)
n1 = MathTex('f(t) = A \cdot sin(\omega \cdot t)').move_to([-3,1.5,0]).set_color_by_gradient([RED, WHITE]).scale(1.2)
n2 = MathTex('g(t) = A \cdot cos(\omega \cdot t)').move_to([3.5,1.5,0]).set_color_by_gradient([RED, WHITE]).scale(1.2)
n3 = Tex('\\textit{Senoides}', color = YELLOW).move_to([-3,-0.5,0]).scale(1.5)
n4 = Tex('\\textit{Cossenoides}', color = YELLOW).move_to([3.5,-0.5,0]).scale(1.5)
n5 = Tex('\\textsc{Domínio do tempo}', opacity = 1).move_to([0,-2.5,0]).set_color_by_gradient([GRAY, WHITE])
ne4 = MathTex('F( \\theta)=sin( \\theta)').move_to([-3,1.5,0]).scale(1.2).set_color_by_gradient([BLUE, WHITE])
n6 = MathTex('G( \\theta)=cos( \\theta)').move_to([3,1.5,0]).scale(1.2).set_color_by_gradient([BLUE, WHITE])
n7 = Tex('\\textsc{Domínio do Ângulo}').move_to([0,-1,0]).set_color_by_gradient([GRAY, WHITE])
n8 = Tex('\\textit{Mudar Domínio}').move_to([0,-2,0]).scale(1.5)
n9 = MathTex('G(t)=cos(t)').move_to([0,0,0]).set_color_by_gradient([YELLOW, WHITE]).scale(1.2)
def f1(x):
return Ac1.get_value()*np.cos(x)
def f2(x):
return Ac2.get_value()*np.cos(x)
E1 = Axes(x_range = [-9,9,2], y_range = [-2,3,1] , x_length = 4, y_length = 3).move_to([-3.5,0,0])
n10 = always_redraw(lambda: MathTex('y').next_to( E1, UP, buff = 0 ).shift(0.3*LEFT+0.2*DOWN) )
n11 = always_redraw(lambda: MathTex('\\theta').next_to( E1, RIGHT, buff = 0).shift(0.5*DOWN) )
c1 = E1.plot(lambda x: f1(x), x_range = [-7,7], color = BLUE)
E2 = Axes(x_range = [-9,9,2], y_range = [-2,3,1] , x_length = 4, y_length = 3).move_to([3.5,0,0])
n12 = always_redraw(lambda: MathTex('y').next_to( E2, UP, buff = 0 ).shift(0.3*LEFT+0.2*DOWN) )
n13 = always_redraw(lambda: MathTex('t').next_to( E2, RIGHT, buff = 0).shift(0.5*DOWN) )
c2 = E2.plot(lambda x: f2(x), x_range = [-7,7], color = YELLOW)
G0 = VGroup(E1,n10,n11,n6, c1)
G1 = VGroup(E2, n12,n9,n13, c2)
ne = Text('A - Amplitude').move_to([0,3,0])
######################################################### Equação envolvendo amplitude
ne01 = MathTex('A \\cdot G(t)=').move_to([3.4,1.5,0])
ne02 = MathTex('cos(t)').next_to(ne01, RIGHT, buff = 0.7)
ne1 = VGroup(ne01,ne02)
#########################################################
# CRIAR OBJETO n14. OBJETO QUE SIMULA UMA CONTAGEM NUMÉRICA NA TELA.
######################################################### Plano que cobre a cena
def cobrir_cena(x):
retangulo = Rectangle().scale(2).set_opacity(0.7).set_color(BLACK)
if x ==1:
return self.play(FadeIn(retangulo))
if x ==0:
return self.play(FadeOut(retangulo))
#################################################################################
# n14 criar contador numérico
n14 = DecimalNumber(1)
n14.add_updater(lambda d: d.set_value(Ac2.get_value()))
n15 = MathTex('-1\leqslant cos(t)\leqslant 1').move_to([0,0,0])
n16 = MathTex('-A\leqslant A\cdot cos(t)\leqslant A').move_to([0,0,0])
# n17 criar contador numérico
n17 = DecimalNumber(1)
n17.add_updater(lambda d: d.set_value(w2.get_value()))
n18_0 = MathTex('G(\\omega \\cdot t)=cos(').move_to([3.8,1.8,0])
n18_1 = MathTex('t)').next_to(n18_0, RIGHT, buff = 0.6)
n18 = VGroup(n18_0, n18_1)
n19_0 = MathTex('\\omega').move_to([-3,3,0]).scale(2)
n19_1 = Text(' - Velocidade Angular').next_to(n19_0, RIGHT, buff = 0.2)
n19 = VGroup(n19_0,n19_1)
caux1=E1.plot(lambda x: f1(x), x_range = [0,2*PI], color = GREEN, stroke_width = 10 )
caux2=E2.plot(lambda x: f2(x), x_range = [0,(2*PI)/w2.get_value()], color = GREEN, stroke_width = 10)
n22 = MathTex('G(\\theta) = G(\\omega \\cdot t)').move_to([0,0,0])
n23 = MathTex('\\theta =\\omega \\cdot t').move_to([0,0,0])
n24 = MathTex('\\omega').move_to([-0.5,0,0])
n25 = MathTex('=').next_to(n24, RIGHT, buff = 0.2)
n26 = MathTex('\\frac{\\theta}{t}').next_to(n25, RIGHT, buff = 0.2)
n28 = MathTex('\\frac{\\bigtriangleup \\theta }{\\bigtriangleup t }').move_to(n26.get_center()+0.2*RIGHT)
n30 = MathTex('T')
n31 = MathTex('\\frac{2 \\pi}{\\bigtriangleup t}')
n32 = MathTex('\\frac{2 \\pi}{\\bigtriangleup t}')
n33 = MathTex('T = \\frac{2 \\pi}{\\omega}')
G02 = VGroup(n24,n25,n28)
G2 = VGroup(n24,n25,n32)
n34_0 = MathTex('f').scale(2)
n34_1 = Text(' - Frequência Angular ').next_to(n34_0, RIGHT, buff = 0.2)
n34 = VGroup(n34_0, n34_1)
n35_0 = Text('N° de ciclos que')
n35_1 = Text('ocorrem em 1 segundo ').next_to(n34_0, DOWN, buff = 0.2)
n35 = VGroup(n35_0, n35_1)
n36 = MathTex('f = \\frac{1}{T}')
n37 = MathTex('T = \\frac{2 \\pi}{\\omega}')
n38 = MathTex('f = \\frac{\\omega}{2 \\pi}')
n39 = MathTex('\\omega = 2 \\pi f')
ne3_0 = MathTex('\\phi').scale(2)
ne3_1 = Text(' - Ângulo de Fase ').next_to(n34_0, RIGHT, buff = 0.2)
ne3= VGroup(ne3_0, ne3_1)
n40_0 = MathTex('G(\\theta + \\phi) = cos(\\theta ')
n40_1 = MathTex(' )').next_to(n40_0, RIGHT, buff = 0.6)
n40 = VGroup(n40_0, n40_1)
# criar n41 contador
n41 = DecimalNumber(0)
n41.add_updater(lambda d: d.set_value(w1.get_value()))
n42_0 = MathTex('G(t +\\phi) = cos(t ')
n42_1 = MathTex(' )').next_to(n42_0, RIGHT, buff = 0.6)
n42 = VGroup(n42_0, n42_1)
# criar n43 contador
n43 = DecimalNumber(0)
n43.add_updater(lambda d: d.set_value(w1.get_value()))
n44 = MathTex('\\phi')
n45 = MathTex('\\phi')
n46 = MathTex('\\phi')
n47 = MathTex('\\phi')
# criar v2 v3 v4 v5
v1_0 = Arrow([0,0,0],[-1,0,0], buff=0)
v1_1 = Arrow([0,0,0],[1,0,0], buff=0)
v1 = VGroup(v1_0, v1_1)
v2 = Arrow(E1.c2p(-0.1,-1.5,0),E1.c2p(-3,-1.5,0), buff=0)
v3 = Arrow(E1.c2p(0.1,-1.5,0),E1.c2p(3,-1.5,0), buff=0)
v4 = Arrow(E2.c2p(-0.1,-1.5,0),E2.c2p(-3,-1.5,0), buff=0)
v5 = Arrow(E2.c2p(0.1,-1.5,0),E2.c2p(3,-1.5,0), buff=0)
n48 = MathTex('G(\\omega t +\\phi) = cos(\\omega t + \\phi) ')
n51 = MathTex('A \\cdot cos(\\omega t + \\phi) ')
n52 = MathTex('g(t)=A \\cdot cos(\\omega \\cdot t + \\phi) ')
L1 = E2.get_vertical_line(E2.i2gp(2*PI, c2 ), color=YELLOW)
####################################################################################################
# PRODUÇÃO CENAS DINÂMICAS
####################################################################################################
# cena 4
#self.add(n10)
#self.add(n11)
#self.add(E1)
#self.add(c1)
n7.move_to([-3.5,-3,0])
#self.add(n7)
n6.move_to([-1.5,2,0])
#self.add(n6)
#self.add(n12)
#self.add(n13)
#self.add(E2)
#self.add(c2)
n5.move_to([3.5,-3,0])
#self.add(n5)
n9.move_to([5.3,2,0])
#self.add(n9)
G1.shift(0.5*LEFT)
g6 = VGroup(E1,n10,n11)
self.play(DrawBorderThenFill(g6))
self.play(Write(n6), run_time = 1.5)
self.play(Write(c1), run_time = 1.5)
self.play(Write(n7))
g7 = VGroup(E2,n12,n13)
self.play(DrawBorderThenFill(g7))
self.play(Write(n9))
self.play(Write(c2))
self.play(Write(n5))
%%manim -qm -v WARNING senoide_estatica3
class senoide_estatica3(Scene):
def construct(self):
##############################################################################
# CRIAR OBJETOS MANIM
##############################################################################
Ac1 = ValueTracker(1) # rastreador da amplitude c1
w1 = ValueTracker(1)
phic1 = ValueTracker(0)
Ac2 = ValueTracker(1) # rastreador da amplitude c2
w2 = ValueTracker(1)
phic2 = ValueTracker(0)
n1 = MathTex('f(t) = A \cdot sin(\omega \cdot t)').move_to([-3,1.5,0]).set_color_by_gradient([RED, WHITE]).scale(1.2)
n2 = MathTex('g(t) = A \cdot cos(\omega \cdot t)').move_to([3.5,1.5,0]).set_color_by_gradient([RED, WHITE]).scale(1.2)
n3 = Tex('\\textit{Senoides}', color = YELLOW).move_to([-3,-0.5,0]).scale(1.5)
n4 = Tex('\\textit{Cossenoides}', color = YELLOW).move_to([3.5,-0.5,0]).scale(1.5)
n5 = Tex('\\textsc{Domínio do tempo}', opacity = 1).move_to([0,-2.5,0]).set_color_by_gradient([GRAY, WHITE])
ne4 = MathTex('F( \\theta)=sin( \\theta)').move_to([-3,1.5,0]).scale(1.2).set_color_by_gradient([BLUE, WHITE])
n6 = MathTex('G( \\theta)=cos( \\theta)').move_to([3,1.5,0]).scale(1.2).set_color_by_gradient([BLUE, WHITE])
n7 = Tex('\\textsc{Domínio do Ângulo}').move_to([0,-1,0]).set_color_by_gradient([GRAY, WHITE])
n8 = Tex('\\textit{Mudar Domínio}').move_to([0,-2,0]).scale(1.5)
n9 = MathTex('G(t)=cos(t)').move_to([0,0,0]).set_color_by_gradient([YELLOW, WHITE]).scale(1.2)
def f1(x):
return Ac1.get_value()*np.cos(x)
def f2(x):
return Ac2.get_value()*np.cos(x)
E1 = Axes(x_range = [-9,9,2], y_range = [-2,3,1] , x_length = 4, y_length = 3).move_to([-3.5,0,0])
n10 = always_redraw(lambda: MathTex('y').next_to( E1, UP, buff = 0 ).shift(0.3*LEFT+0.2*DOWN) )
n11 = always_redraw(lambda: MathTex('\\theta').next_to( E1, RIGHT, buff = 0).shift(0.5*DOWN) )
c1 = always_redraw(lambda: E1.plot(lambda x: f1(x), x_range = [-7,7], color = BLUE))
E2 = Axes(x_range = [-9,9,2], y_range = [-2,3,1] , x_length = 4, y_length = 3).move_to([3.5,0,0])
n12 = always_redraw(lambda: MathTex('y').next_to( E2, UP, buff = 0 ).shift(0.3*LEFT+0.2*DOWN) )
n13 = always_redraw(lambda: MathTex('t').next_to( E2, RIGHT, buff = 0).shift(0.5*DOWN) )
c2 = always_redraw(lambda:E2.plot(lambda x: f2(x), x_range = [-7,7], color = YELLOW))
G0 = VGroup(E1,n10,n11,n6, c1)
G1 = VGroup(E2, n12,n9,n13, c2)
ne = Tex('\\textit{A - Amplitude}').move_to([0,3,0]).scale(1.5)
######################################################### Equação envolvendo amplitude
ne01 = MathTex('A \\cdot G(t)=').move_to([3.4,1.5,0])
ne02 = MathTex('cos(t)').next_to(ne01, RIGHT, buff = 0.7)
ne1 = VGroup(ne01,ne02).set_color_by_gradient([YELLOW, WHITE])
#########################################################
# CRIAR OBJETO n14. OBJETO QUE SIMULA UMA CONTAGEM NUMÉRICA NA TELA.
######################################################### Plano que cobre a cena
retangulo = Rectangle().scale(4).set_opacity(0.9).set_color(BLACK).move_to([0,0,1])
def cobrir_cena(x):
if x ==1:
return self.play(FadeIn(retangulo))
else:
return self.play(FadeOut(retangulo))
#################################################################################
n15 = MathTex('-1\leqslant cos(t)\leqslant 1').move_to([0,0,0]).scale(2).set_color_by_gradient([WHITE,GREEN_E])
n16 = MathTex('-A\leqslant A\cdot cos(t)\leqslant A').move_to([0,0,0]).scale(2).set_color_by_gradient([WHITE,GREEN_E])
# n17 criar contador numérico
n17 = DecimalNumber(1)
n17.add_updater(lambda d: d.set_value(w2.get_value()).scale(0.5))
n18_0 = MathTex('G(\\omega \\cdot t)=cos(').move_to([3.8,1.8,0])
n18_1 = MathTex('t)').next_to(n18_0, RIGHT, buff = 0.6)
n18 = VGroup(n18_0, n18_1)
n19_0 = MathTex('\\omega').move_to([-3,3,0]).scale(2)
n19_1 = Text(' - Velocidade Angular').next_to(n19_0, RIGHT, buff = 0.2)
n19 = VGroup(n19_0,n19_1)
caux1=E1.plot(lambda x: f1(x), x_range = [0,2*PI], color = GREEN, stroke_width = 10 )
caux2=E2.plot(lambda x: f2(x), x_range = [0,(2*PI)/w2.get_value()], color = GREEN, stroke_width = 10)
n22 = MathTex('G(\\theta) = G(\\omega \\cdot t)').move_to([0,0,0])
n23 = MathTex('\\theta =\\omega \\cdot t').move_to([0,0,0])
n24 = MathTex('\\omega').move_to([-0.5,0,0])
n25 = MathTex('=').next_to(n24, RIGHT, buff = 0.2)
n26 = MathTex('\\frac{\\theta}{t}').next_to(n25, RIGHT, buff = 0.2)
n28 = MathTex('\\frac{\\bigtriangleup \\theta }{\\bigtriangleup t }').move_to(n26.get_center()+0.2*RIGHT)
n30 = MathTex('T')
n31 = MathTex('\\frac{2 \\pi}{\\bigtriangleup t}')
n32 = MathTex('\\frac{2 \\pi}{\\bigtriangleup t}')
n33 = MathTex('T = \\frac{2 \\pi}{\\omega}')
G02 = VGroup(n24,n25,n28)
G2 = VGroup(n24,n25,n32)
n34_0 = MathTex('f').scale(2)
n34_1 = Text(' - Frequência Angular ').next_to(n34_0, RIGHT, buff = 0.2)
n34 = VGroup(n34_0, n34_1)
n35_0 = Text('N° de ciclos que')
n35_1 = Text('ocorrem em 1 segundo ').next_to(n34_0, DOWN, buff = 0.2)
n35 = VGroup(n35_0, n35_1)
n36 = MathTex('f = \\frac{1}{T}')
n37 = MathTex('T = \\frac{2 \\pi}{\\omega}')
n38 = MathTex('f = \\frac{\\omega}{2 \\pi}')
n39 = MathTex('\\omega = 2 \\pi f')
ne3_0 = MathTex('\\phi').scale(2)
ne3_1 = Text(' - Ângulo de Fase ').next_to(n34_0, RIGHT, buff = 0.2)
ne3= VGroup(ne3_0, ne3_1)
n40_0 = MathTex('G(\\theta + \\phi) = cos(\\theta ')
n40_1 = MathTex(' )').next_to(n40_0, RIGHT, buff = 0.6)
n40 = VGroup(n40_0, n40_1)
# criar n41 contador
n41 = DecimalNumber(0)
n41.add_updater(lambda d: d.set_value(w1.get_value()))
n42_0 = MathTex('G(t +\\phi) = cos(t ')
n42_1 = MathTex(' )').next_to(n42_0, RIGHT, buff = 0.6)
n42 = VGroup(n42_0, n42_1)
# criar n43 contador
n43 = DecimalNumber(0)
n43.add_updater(lambda d: d.set_value(w1.get_value()))
n44 = MathTex('\\phi')
n45 = MathTex('\\phi')
n46 = MathTex('\\phi')
n47 = MathTex('\\phi')
# criar v2 v3 v4 v5
v1_0 = Arrow([0,0,0],[-1,0,0], buff=0)
v1_1 = Arrow([0,0,0],[1,0,0], buff=0)
v1 = VGroup(v1_0, v1_1)
v2 = Arrow(E1.c2p(-0.1,-1.5,0),E1.c2p(-3,-1.5,0), buff=0)
v3 = Arrow(E1.c2p(0.1,-1.5,0),E1.c2p(3,-1.5,0), buff=0)
v4 = Arrow(E2.c2p(-0.1,-1.5,0),E2.c2p(-3,-1.5,0), buff=0)
v5 = Arrow(E2.c2p(0.1,-1.5,0),E2.c2p(3,-1.5,0), buff=0)
n48 = MathTex('G(\\omega t +\\phi) = cos(\\omega t + \\phi) ')
n51 = MathTex('A \\cdot cos(\\omega t + \\phi) ')
n52 = MathTex('g(t)=A \\cdot cos(\\omega \\cdot t + \\phi) ')
L1 = E2.get_vertical_line(E2.i2gp(2*PI, c2 ), color=YELLOW)
####################################################################################################
# PRODUÇÃO CENAS DINÂMICAS
####################################################################################################
##################### imagem da cena 4(atualize este código)
self.add(n10)
self.add(n11)
self.add(E1)
self.add(c1)
n7.move_to([-3.5,-3,0])
self.add(n7)
n6.move_to([-1.5,1.5,0])
self.add(n6)
self.add(n12)
self.add(n13)
self.add(E2)
self.add(c2)
n5.move_to([3.5,-3,0])
self.add(n5)
n9.move_to([5.3,1.5,0])
self.add(n9)
#############################################################
#self.add(ne) # rótulo da amplitude
G0.shift(0.5*LEFT)
G1.shift(1.5*LEFT)
# n14 criar contador numérico
n141 = MathTex('1').next_to(ne01, RIGHT, buff = 0.1)
n142 = MathTex('2').next_to(ne01, RIGHT, buff = 0.1)
n1406 = MathTex('0.6').next_to(ne01, RIGHT, buff = 0.1)
n140 = MathTex('0').next_to(ne01, RIGHT, buff = 0.1)
n14m1 = MathTex('-1').next_to(ne01, RIGHT, buff = 0.1)
n141m = MathTex('1').next_to(ne01, RIGHT, buff = 0.1)
#self.add(ne1) # rótulo da cossenoide com amplitude variável
#self.add(n14)
self.play(Write(ne), run_time = 2)
self.play(ReplacementTransform(n9, ne1), run_time = 1.5)
self.play(Write(n141), run_time = 1.5)
self.wait(9)
self.play(Ac2.animate.set_value(2), Transform(n141,n142), run_time = 5)
self.play(Ac2.animate.set_value(0.6),Transform(n141,n1406), run_time = 4)
self.play(Ac2.animate.set_value(0), Transform(n141,n140))
self.play(Ac2.animate.set_value(-1),Transform(n141,n14m1), run_time = 4)
self.play(Ac2.animate.set_value(1),Transform(n141,n141m), run_time = 4 )
self.wait()
cobrir_cena(1)
self.wait(8)
self.play(Write(n15))
self.wait(3)
self.play(ReplacementTransform(n15, n16), run_time = 3)
self.wait(6)
self.play(FadeOut(n16), run_time = 2)
self.remove(ne,n141,ne1)
cobrir_cena(0)
self.wait()
%%manim -qm -v WARNING senoide_estatica04
class senoide_estatica04(Scene):
def construct(self):
##############################################################################
# CRIAR OBJETOS MANIM
##############################################################################
Ac1 = ValueTracker(1) # rastreador da amplitude c1
w1 = ValueTracker(1)
phic1 = ValueTracker(0)
Ac2 = ValueTracker(1) # rastreador da amplitude c2
w2 = ValueTracker(1)
phic2 = ValueTracker(0)
n1 = MathTex('f(t) = A \cdot sin(\omega \cdot t)').move_to([-3,1.5,0]).set_color_by_gradient([RED, WHITE]).scale(1.2)
n2 = MathTex('g(t) = A \cdot cos(\omega \cdot t)').move_to([3.5,1.5,0]).set_color_by_gradient([RED, WHITE]).scale(1.2)
n3 = Tex('\\textit{Senoides}', color = YELLOW).move_to([-3,-0.5,0]).scale(1.5)
n4 = Tex('\\textit{Cossenoides}', color = YELLOW).move_to([3.5,-0.5,0]).scale(1.5)
n5 = Tex('\\textsc{Domínio do tempo}', opacity = 1).move_to([0,-2.5,0]).set_color_by_gradient([GRAY, WHITE])
ne4 = MathTex('F( \\theta)=sin( \\theta)').move_to([-3,1.5,0]).scale(1.2).set_color_by_gradient([BLUE, WHITE])
n6 = MathTex('G( \\theta)=cos( \\theta)').move_to([3,1.5,0]).scale(1.2).set_color_by_gradient([BLUE, WHITE])
n7 = Tex('\\textsc{Domínio do Ângulo}').move_to([0,-1,0]).set_color_by_gradient([GRAY, WHITE])
n8 = Tex('\\textit{Mudar Domínio}').move_to([0,-2,0]).scale(1.5)
n9 = MathTex('G(t)=cos(t)').move_to([0,0,0]).set_color_by_gradient([YELLOW, WHITE]).scale(1.2)
def f1(x):
return Ac1.get_value()*np.cos(x)
def f2(x):
return Ac2.get_value()*np.cos(w2.get_value()*x)
E1 = Axes(x_range = [-9,9,2], y_range = [-2,3,1] , x_length = 4, y_length = 3).move_to([-3.5,0,0])
n10 = always_redraw(lambda: MathTex('y').next_to( E1, UP, buff = 0 ).shift(0.3*LEFT+0.2*DOWN) )
n11 = always_redraw(lambda: MathTex('\\theta').next_to( E1, RIGHT, buff = 0).shift(0.5*DOWN) )
c1 = E1.plot(lambda x: f1(x), x_range = [-7,7], color = BLUE)
E2 = Axes(x_range = [-9,9,2], y_range = [-2,3,1] , x_length = 4, y_length = 3).move_to([3.5,0,0])
n12 = always_redraw(lambda: MathTex('y').next_to( E2, UP, buff = 0 ).shift(0.3*LEFT+0.2*DOWN) )
n13 = always_redraw(lambda: MathTex('t').next_to( E2, RIGHT, buff = 0).shift(0.5*DOWN) )
c2 = always_redraw(lambda: E2.plot(lambda x: f2(x), x_range = [-7,7], color = YELLOW))
G0 = VGroup(E1,n10,n11,n6, c1)
G1 = VGroup(E2, n12,n9,n13, c2)
ne = Tex('\\textit{A - Amplitude}').move_to([0,3,0]).scale(1.5)
######################################################### Equação envolvendo amplitude
ne01 = MathTex('A \\cdot G(t)=').move_to([3.4,1.5,0])
ne02 = MathTex('cos(t)').next_to(ne01, RIGHT, buff = 0.7)
ne1 = VGroup(ne01,ne02)
#########################################################
# CRIAR OBJETO n14. OBJETO QUE SIMULA UMA CONTAGEM NUMÉRICA NA TELA.
######################################################### Plano que cobre a cena
retangulo = Rectangle().scale(4).set_opacity(0.9).set_color(BLACK).move_to([0,0,1])
def cobrir_cena(x):
if x ==1:
return self.play(FadeIn(retangulo))
else:
return self.play(FadeOut(retangulo))
#################################################################################
# n14 criar contador numérico
n14 = DecimalNumber(1).scale(0.7)
n14.add_updater(lambda d: d.set_value(Ac2.get_value()))
n15 = MathTex('-1\leqslant cos(t)\leqslant 1').move_to([0,0,0])
n16 = MathTex('-A\leqslant A\cdot cos(t)\leqslant A').move_to([0,0,0])
# n17 criar contador numérico
n17 = DecimalNumber(0)
n17.add_updater(lambda d: d.set_value(w2.get_value()).scale(0.5))
n18_0 = MathTex('G(\\omega \\cdot t)=cos(').move_to([3.8,1.8,0])
n18_1 = MathTex('t)').next_to(n18_0, RIGHT, buff = 0.75)
n18 = VGroup(n18_0, n18_1).set_color_by_gradient([YELLOW, WHITE])
n19_0 = MathTex('\\omega').move_to([-3,3,0]).scale(2)
n19_1 = Tex('\\textit {- Velocidade Angular}').scale(1.5).next_to(n19_0, RIGHT, buff = 0.2)
n19 = VGroup(n19_0,n19_1)
caux1=E1.plot(lambda x: f1(x), x_range = [0,2*PI], color = GREEN, stroke_width = 10 )
caux2=E2.plot(lambda x: f2(x), x_range = [0,(2*PI)/w2.get_value()], color = GREEN, stroke_width = 10)
n22 = MathTex('G(\\theta) = G(\\omega \\cdot t)').move_to([0,0,0]).scale(2).set_color_by_gradient([WHITE,GREEN_E])
n23 = MathTex('\\theta =\\omega \\cdot t').move_to([0,0,0]).scale(2).set_color_by_gradient([WHITE,GREEN_E])
n24 = MathTex('\\omega').move_to([-0.5,0,0]).scale(2).set_color_by_gradient([WHITE,GREEN_E])
n25 = MathTex('=').scale(2).set_color_by_gradient([WHITE,GREEN_E]).next_to(n24, RIGHT, buff = 0.2)
n26 = MathTex('\\frac{\\theta}{t}').scale(2).set_color_by_gradient([WHITE,GREEN_E]).next_to(n25, RIGHT, buff = 0.2)
n28 = MathTex('\\frac{\\bigtriangleup \\theta }{\\bigtriangleup t }').move_to(n26.get_center()+0.3*RIGHT).scale(2).set_color_by_gradient([WHITE,GREEN_E])
n30 = MathTex('T').scale(2).set_color_by_gradient([WHITE,GREEN_E])
n31 = MathTex('\\frac{2 \\pi}{\\bigtriangleup t}').scale(2).set_color_by_gradient([WHITE,GREEN_E])
n32 = MathTex('\\frac{2 \\pi}{\\bigtriangleup t}').scale(2).set_color_by_gradient([WHITE,GREEN_E])
n33 = MathTex('T = \\frac{2 \\pi}{\\omega}').scale(2).set_color_by_gradient([WHITE,GREEN_E])
G02 = VGroup(n24,n25,n28)
G2 = VGroup(n24,n25,n32)
n34_0 = MathTex('f').scale(2)
n34_1 = Text(' - Frequência Angular ').next_to(n34_0, RIGHT, buff = 0.2)
n34 = VGroup(n34_0, n34_1)
n35_0 = Text('N° de ciclos que')
n35_1 = Text('ocorrem em 1 segundo ').next_to(n34_0, DOWN, buff = 0.2)
n35 = VGroup(n35_0, n35_1)
n36 = MathTex('f = \\frac{1}{T}')
n37 = MathTex('T = \\frac{2 \\pi}{\\omega}')
n38 = MathTex('f = \\frac{\\omega}{2 \\pi}')
n39 = MathTex('\\omega = 2 \\pi f')
ne3_0 = MathTex('\\phi').scale(2)
ne3_1 = Text(' - Ângulo de Fase ').next_to(n34_0, RIGHT, buff = 0.2)
ne3= VGroup(ne3_0, ne3_1)
n40_0 = MathTex('G(\\theta + \\phi) = cos(\\theta ')
n40_1 = MathTex(' )').next_to(n40_0, RIGHT, buff = 0.6)
n40 = VGroup(n40_0, n40_1)
# criar n41 contador
n41 = DecimalNumber(0)
n41.add_updater(lambda d: d.set_value(w1.get_value()))
n42_0 = MathTex('G(t +\\phi) = cos(t ')
n42_1 = MathTex(' )').next_to(n42_0, RIGHT, buff = 0.6)
n42 = VGroup(n42_0, n42_1)
# criar n43 contador
n43 = DecimalNumber(0)
n43.add_updater(lambda d: d.set_value(w1.get_value()))
n44 = MathTex('\\phi')
n45 = MathTex('\\phi')
n46 = MathTex('\\phi')
n47 = MathTex('\\phi')
# criar v2 v3 v4 v5
v1_0 = Arrow([0,0,0],[-1,0,0], buff=0)
v1_1 = Arrow([0,0,0],[1,0,0], buff=0)
v1 = VGroup(v1_0, v1_1)
v2 = Arrow(E1.c2p(-0.1,-1.5,0),E1.c2p(-3,-1.5,0), buff=0)
v3 = Arrow(E1.c2p(0.1,-1.5,0),E1.c2p(3,-1.5,0), buff=0)
v4 = Arrow(E2.c2p(-0.1,-1.5,0),E2.c2p(-3,-1.5,0), buff=0)
v5 = Arrow(E2.c2p(0.1,-1.5,0),E2.c2p(3,-1.5,0), buff=0)
n48 = MathTex('G(\\omega t +\\phi) = cos(\\omega t + \\phi) ')
n51 = MathTex('A \\cdot cos(\\omega t + \\phi) ')
n52 = MathTex('g(t)=A \\cdot cos(\\omega \\cdot t + \\phi) ')
L1 = E2.get_vertical_line(E2.i2gp(2*PI, c2 ), color=YELLOW)
####################################################################################################
# PRODUÇÃO CENAS DINÂMICAS
####################################################################################################
#cena 9
############################## cena 4(atualize este código)
self.add(n10)
self.add(n11)
self.add(E1)
self.add(c1)
n7.move_to([-3.5,-3,0])
self.add(n7)
n6.move_to([-1.5,2,0])
self.add(n6)
self.add(n12)
self.add(n13)
self.add(E2)
self.add(c2)
n5.move_to([3.5,-3,0])
self.add(n5)
n9.move_to([5.3,2,0])
#self.add(n9)
###########################################################
G0.shift(0.5*LEFT)
G1.shift(1.5*LEFT)
#self.add(n18)
#self.add(n19)
self.play(FadeIn(n9))
self.wait(2)
self.play(Write(n19), run_time = 4)
n9_1= n9.copy()
self.play(Transform(n9, n18))
# n17 criar contador numérico
n171 = MathTex('1').next_to(n18_0, RIGHT, buff = 0.1)
n172 = MathTex('2').next_to(n18_0, RIGHT, buff = 0.1)
n1702 = MathTex('0.2').next_to(n18_0, RIGHT, buff = 0.1)
n171m = MathTex('1').next_to(n18_0, RIGHT, buff = 0.1)
self.play(Write(n171))
self.wait(6)
self.play(w2.animate.set_value(2), Transform(n171,n172), run_time = 6)
self.wait(5)
self.play(w2.animate.set_value(0.2),Transform(n171,n1702), run_time =5)
self.wait(4)
self.play(w2.animate.set_value(1), Transform(n171,n171m))
self.play(Unwrite(n19))
## criar curvas verdes
c1verde = E1.plot( lambda x: f1(x), x_range = [0,2*PI], color = GREEN, stroke_width = 10)
c2verde = always_redraw(lambda: E2.plot(lambda x: f2(x), x_range = [0,2*PI/w2.get_value()], color = GREEN,stroke_width = 10))
self.play( FadeIn(c1verde), FadeIn(c2verde) )
# criar linhas verticais
n172 = MathTex('2').next_to(n18_0, RIGHT, buff = 0.1)
self.play(w2.animate.set_value(2), Transform(n171,n172), run_time = 4)
lineV1 = always_redraw( lambda: E1.get_vertical_line( E1.c2p(2*PI,f1(2*PI)) , line_func = Line) )
lineV2 = always_redraw( lambda: E2.get_vertical_line( E2.c2p(PI,f2(2*PI)) , line_func = Line) )
doispi = MathTex('2 \\pi').next_to( E1.c2p(2*PI,0) , DOWN, buff = 0.1)
pi = MathTex('\\pi').next_to( E2.c2p(PI,0) , DOWN, buff = 0.1)
self.play(Create(lineV1), Create(lineV2))
self.play(Write(doispi), Create(pi))
cobrir_cena(1)
self.remove(c1verde, c2verde, doispi, pi,lineV1, lineV2)
self.wait()
self.play(Write(n22), run_time= 3)
self.wait()
self.play(Transform(n22, n23), run_time= 3)
self.wait(2)
self.play(Transform(n22, n24), run_time = 3)
g2 = VGroup(n25,n26)
self.play(Write(g2))
self.play(Transform(n26, n28), run_time = 2)
self.wait(10)
g3 = VGroup(n22,n25,n26)
self.play(FadeOut(g3), run_time = 4)
cobrir_cena(0)
self.wait(4)
self.play(FadeOut(G0), FadeOut(n7),FadeOut(n5))
G11 = VGroup(G1, n171,n18_0)
self.play(G11.animate.move_to([0,0,0]), run_time = 3)
n172 = MathTex('1').next_to(n18_0, RIGHT, buff = 0.1)
self.play( w2.animate.set_value(1), Transform(n171,n172) )
%%manim -qm -v WARNING senoide_estatica05
class senoide_estatica05(Scene):
def construct(self):
##############################################################################
# CRIAR OBJETOS MANIM
##############################################################################
Ac1 = ValueTracker(1) # rastreador da amplitude c1
w1 = ValueTracker(1)
phic1 = ValueTracker(0)
Ac2 = ValueTracker(1) # rastreador da amplitude c2
w2 = ValueTracker(1)
phic2 = ValueTracker(0)
n1 = MathTex('f(t) = A \cdot sin(\omega \cdot t)').move_to([-3,1.5,0]).set_color_by_gradient([RED, WHITE]).scale(1.2)
n2 = MathTex('g(t) = A \cdot cos(\omega \cdot t)').move_to([3.5,1.5,0]).set_color_by_gradient([RED, WHITE]).scale(1.2)
n3 = Tex('\\textit{Senoides}', color = YELLOW).move_to([-3,-0.5,0]).scale(1.5)
n4 = Tex('\\textit{Cossenoides}', color = YELLOW).move_to([3.5,-0.5,0]).scale(1.5)
n5 = Tex('\\textsc{Domínio do tempo}', opacity = 1).move_to([0,-2.5,0]).set_color_by_gradient([GRAY, WHITE])
ne4 = MathTex('F( \\theta)=sin( \\theta)').move_to([-3,1.5,0]).scale(1.2).set_color_by_gradient([BLUE, WHITE])
n6 = MathTex('G( \\theta)=cos( \\theta)').move_to([3,1.5,0]).scale(1.2).set_color_by_gradient([BLUE, WHITE])
n7 = Tex('\\textsc{Domínio do Ângulo}').move_to([0,-1,0]).set_color_by_gradient([GRAY, WHITE])
n8 = Tex('\\textit{Mudar Domínio}').move_to([0,-2,0]).scale(1.5)
n9 = MathTex('G(t)=cos(t)').move_to([0,0,0]).set_color_by_gradient([YELLOW, WHITE]).scale(1.2)
def f1(x):
return Ac1.get_value()*np.cos(x)
def f2(x):
return Ac2.get_value()*np.cos(w2.get_value()*x)
E1 = Axes(x_range = [-9,9,2], y_range = [-2,3,1] , x_length = 4, y_length = 3).move_to([-3.5,0,0])
n10 = always_redraw(lambda: MathTex('y').next_to( E1, UP, buff = 0 ).shift(0.3*LEFT+0.2*DOWN) )
n11 = always_redraw(lambda: MathTex('\\theta').next_to( E1, RIGHT, buff = 0).shift(0.5*DOWN) )
c1 = E1.plot(lambda x: f1(x), x_range = [-7,7], color = BLUE)
E2 = Axes(x_range = [-9,9,2], y_range = [-2,3,1] , x_length = 4, y_length = 3).move_to([3.5,0,0])
n12 = always_redraw(lambda: MathTex('y').next_to( E2, UP, buff = 0 ).shift(0.3*LEFT+0.2*DOWN) )
n13 = always_redraw(lambda: MathTex('t').next_to( E2, RIGHT, buff = 0).shift(0.5*DOWN) )
c2 = always_redraw(lambda: E2.plot(lambda x: f2(x), x_range = [-7,7], color = YELLOW))
G0 = VGroup(E1,n10,n11,n6, c1)
G1 = VGroup(E2, n12,n9,n13, c2)
ne = Tex('\\textit{A - Amplitude}').move_to([0,3,0]).scale(1.5)
######################################################### Equação envolvendo amplitude
ne01 = MathTex('A \\cdot G(t)=').move_to([3.4,1.5,0])
ne02 = MathTex('cos(t)').next_to(ne01, RIGHT, buff = 0.7)
ne1 = VGroup(ne01,ne02)
#########################################################
# CRIAR OBJETO n14. OBJETO QUE SIMULA UMA CONTAGEM NUMÉRICA NA TELA.
######################################################### Plano que cobre a cena
retangulo = Rectangle().scale(4).set_opacity(0.9).set_color(BLACK).move_to([0,0,1])
def cobrir_cena(x):
if x ==1:
return self.play(FadeIn(retangulo))
else:
return self.play(FadeOut(retangulo))
#################################################################################
# n14 criar contador numérico
n14 = DecimalNumber(1).scale(0.7)
n14.add_updater(lambda d: d.set_value(Ac2.get_value()))
n15 = MathTex('-1\leqslant cos(t)\leqslant 1').move_to([0,0,0])
n16 = MathTex('-A\leqslant A\cdot cos(t)\leqslant A').move_to([0,0,0])
# n17 criar contador numérico
n17 = DecimalNumber(0)
n17.add_updater(lambda d: d.set_value(w2.get_value()).scale(0.5))
n18_0 = MathTex('G(\\omega \\cdot t)=cos(').move_to([3.8,1.8,0])
n18_1 = MathTex('t)').next_to(n18_0, RIGHT, buff = 0.75)
n18 = VGroup(n18_0, n18_1).set_color_by_gradient([YELLOW, WHITE])
n19_0 = MathTex('\\omega').move_to([-3,3,0]).scale(2)
n19_1 = Tex('\\textit {- Velocidade Angular}').scale(1.5).next_to(n19_0, RIGHT, buff = 0.2)
n19 = VGroup(n19_0,n19_1)
caux1=E1.plot(lambda x: f1(x), x_range = [0,2*PI], color = GREEN, stroke_width = 10 )
caux2=E2.plot(lambda x: f2(x), x_range = [0,(2*PI)/w2.get_value()], color = GREEN, stroke_width = 10)
n22 = MathTex('G(\\theta) = G(\\omega \\cdot t)').move_to([0,0,0])
n23 = MathTex('\\theta =\\omega \\cdot t').move_to([0,0,0])
n24 = MathTex('\\omega').move_to([-0.5,0,0])
n25 = MathTex('=').next_to(n24, RIGHT, buff = 0.2)
n26 = MathTex('\\frac{\\theta}{t}').next_to(n25, RIGHT, buff = 0.2)
n28 = MathTex('\\frac{\\bigtriangleup \\theta }{\\bigtriangleup t }').move_to(n26.get_center()+0.2*RIGHT)
n30 = MathTex('T')
n31 = MathTex('\\frac{2 \\pi}{\\bigtriangleup t}')
n32 = MathTex('\\frac{2 \\pi}{T}')
n33 = MathTex('T = \\frac{2 \\pi}{\\omega}')
G02 = VGroup(n24,n25,n28).set_color_by_gradient([WHITE,GREEN_E])
G2 = VGroup(n24,n25,n32).set_color_by_gradient([WHITE,GREEN_E])
n34_0 = MathTex('f').scale(2)
n34_1 = Tex(' - Frequência Angular ').scale(1.5).next_to(n34_0, RIGHT, buff = 0.2)
n34 = VGroup(n34_0, n34_1)
n35_0 = Tex('N° de ciclos que').scale(1.5)
n35_1 = Tex('ocorrem em 1 segundo ').scale(1.5).next_to(n34_0, DOWN, buff = 0.2)
n35 = VGroup(n35_0, n35_1)
n36 = MathTex('f = \\frac{1}{T}').scale(2).set_color_by_gradient([WHITE,GREEN_E])
n37 = MathTex('T = \\frac{2 \\pi}{\\omega}').scale(2).set_color_by_gradient([WHITE,GREEN_E])
n38 = MathTex('f = \\frac{\\omega}{2 \\pi}').scale(2).set_color_by_gradient([WHITE,GREEN_E])
n39 = MathTex('\\omega = 2 \\pi f').scale(2).set_color_by_gradient([WHITE,GREEN_E])
ne3_0 = MathTex('\\phi').scale(2)
ne3_1 = Text(' - Ângulo de Fase ').next_to(n34_0, RIGHT, buff = 0.2)
ne3= VGroup(ne3_0, ne3_1)
n40_0 = MathTex('G(\\theta + \\phi) = cos(\\theta ')
n40_1 = MathTex(' )').next_to(n40_0, RIGHT, buff = 0.6)
n40 = VGroup(n40_0, n40_1)
# criar n41 contador
n41 = DecimalNumber(0)
n41.add_updater(lambda d: d.set_value(w1.get_value()))
n42_0 = MathTex('G(t +\\phi) = cos(t ')
n42_1 = MathTex(' )').next_to(n42_0, RIGHT, buff = 0.6)
n42 = VGroup(n42_0, n42_1)
# criar n43 contador
n43 = DecimalNumber(0)
n43.add_updater(lambda d: d.set_value(w1.get_value()))
n44 = MathTex('\\phi')
n45 = MathTex('\\phi')
n46 = MathTex('\\phi')
n47 = MathTex('\\phi')
# criar v2 v3 v4 v5
v1_0 = Arrow([0,0,0],[-1,0,0], buff=0)
v1_1 = Arrow([0,0,0],[1,0,0], buff=0)
v1 = VGroup(v1_0, v1_1)
v2 = Arrow(E1.c2p(-0.1,-1.5,0),E1.c2p(-3,-1.5,0), buff=0)
v3 = Arrow(E1.c2p(0.1,-1.5,0),E1.c2p(3,-1.5,0), buff=0)
v4 = Arrow(E2.c2p(-0.1,-1.5,0),E2.c2p(-3,-1.5,0), buff=0)
v5 = Arrow(E2.c2p(0.1,-1.5,0),E2.c2p(3,-1.5,0), buff=0)
n48 = MathTex('G(\\omega t +\\phi) = cos(\\omega t + \\phi) ')
n51 = MathTex('A \\cdot cos(\\omega t + \\phi) ')
n52 = MathTex('g(t)=A \\cdot cos(\\omega \\cdot t + \\phi) ')
L1 = E2.get_vertical_line(E2.i2gp(2*PI, c2 ), color=YELLOW)
####################################################################################################
# PRODUÇÃO CENAS DINÂMICAS
####################################################################################################
#cena 8 e cena 9
############################## cena 4(atualize este código)
self.add(n12)
self.add(n13)
self.add(E2)
self.add(c2)
n5.move_to([3.5,-3,0])
n9.move_to([5.3,2,0])
#self.add(n9)
###########################################################
G1.shift(1.5*LEFT)
self.add(n18)
G1_anterior = G1.copy()
G11 = VGroup(G1,n18)
G11.move_to([0,0,0])
n172 = MathTex('1').next_to(n18_0, RIGHT, buff = 0.1)
self.add(n172)
##############################################################################
n30.next_to(E2.c2p(0,0,0), RIGHT+1.7*DOWN, buff = 0.5)
#self.add(n30) # construir rótulo da seta: período
G02.move_to([3,-1.5,0])
#self.add(G02)
n31.next_to(n25, RIGHT, buff = 0.2)
#self.add(n31)
n32.next_to(n25, RIGHT, buff = 0.2)
n33.move_to(G02.get_center())
#self.add(n33)
n34.move_to([0,2.6,0])
n37.move_to([0,-2.3,0])
L1 = Line(start = E2.c2p(2*PI, f2(2*PI)) , end = E2.c2p(2*PI, -1.2*f2(2*PI)) )
v1_0 = Arrow(E2.c2p(PI,1.2*f2(PI)),E2.c2p(0,-1.2), buff=0)
v1_1 = Arrow(E2.c2p(PI,1.2*f2(PI)),E2.c2p(2*PI,-1.2), buff=0)
v1 = VGroup(v1_0, v1_1)
self.play(FadeIn(v1))
self.play(Write(L1))
self.play(Write(n30))
self.wait(7)
self.play(Write(n24))
self.play(Write(n25))
self.play(Write(n28))
self.wait(2)
self.play(Transform(n28, n31))
self.play(Transform(n28, n32))
self.play(Transform(G02, n33)) # parei aqui
cobrir_cena(1)
self.play( Write(n34))
self.play( Write(n35))
g2 = VGroup( n34,n35)
self.play( Unwrite(g2))
self.play( Write(n36))
self.play( Write(n37))
self.play( n37.animate.move_to(n36))
self.play(FadeOut(n37))
self.play( Transform(n36, n38))
self.play( Transform(n36, n39))
self.play( FadeOut(n36))
# antes descobrir a cena remover alguns objetos e prepara a tela para a cena 16
# da defasagem angular!
### faça isso aqui!!
self.remove(n30,v1,L1,G02,n18,n172)
cobrir_cena(0)
n5.move_to([3.5,-3,0])
n6.move_to([-1.5,2,0])
n7.move_to([-3.5,-3,0])
self.play( FadeIn(G0), G1.animate.move_to(G1_anterior.get_center()), FadeIn(n5), FadeIn(n7) )
%%manim -qm -v WARNING senoide_estatica06
class senoide_estatica06(Scene):
def construct(self):
##############################################################################
# CRIAR OBJETOS MANIM
##############################################################################
Ac1 = ValueTracker(1) # rastreador da amplitude c1
w1 = ValueTracker(1)
phic1 = ValueTracker(0)
Ac2 = ValueTracker(1) # rastreador da amplitude c2
w2 = ValueTracker(1)
phic2 = ValueTracker(0)
n1 = MathTex('f(t) = A \cdot sin(\omega \cdot t)').move_to([-3,1.5,0]).set_color_by_gradient([RED, WHITE]).scale(1.2)
n2 = MathTex('g(t) = A \cdot cos(\omega \cdot t)').move_to([3.5,1.5,0]).set_color_by_gradient([RED, WHITE]).scale(1.2)
n3 = Tex('\\textit{Senoides}', color = YELLOW).move_to([-3,-0.5,0]).scale(1.5)
n4 = Tex('\\textit{Cossenoides}', color = YELLOW).move_to([3.5,-0.5,0]).scale(1.5)
n5 = Tex('\\textsc{Domínio do tempo}', opacity = 1).move_to([0,-2.5,0]).set_color_by_gradient([GRAY, WHITE])
ne4 = MathTex('F( \\theta)=sin( \\theta)').move_to([-3,1.5,0]).scale(1.2).set_color_by_gradient([BLUE, WHITE])
n6 = MathTex('G( \\theta)=cos( \\theta)').move_to([3,1.5,0]).scale(1.2).set_color_by_gradient([BLUE, WHITE])
n7 = Tex('\\textsc{Domínio do Ângulo}').move_to([0,-1,0]).set_color_by_gradient([GRAY, WHITE])
n8 = Tex('\\textit{Mudar Domínio}').move_to([0,-2,0]).scale(1.5)
n9 = MathTex('G(t)=cos(t)').move_to([0,0,0]).set_color_by_gradient([YELLOW, WHITE]).scale(1.2)
def f1(x):
return Ac1.get_value()*np.cos(w1.get_value()*x + phic1.get_value())
def f2(x):
return Ac2.get_value()*np.cos(w2.get_value()*x + phic2.get_value())
E1 = Axes(x_range = [-9,9,2], y_range = [-2,3,1] , x_length = 4, y_length = 3).move_to([-3.5,0,0])
n10 = always_redraw(lambda: MathTex('y').next_to( E1, UP, buff = 0 ).shift(0.3*LEFT+0.2*DOWN) )
n11 = always_redraw(lambda: MathTex('\\theta').next_to( E1, RIGHT, buff = 0).shift(0.5*DOWN) )
c1 = always_redraw(lambda: E1.plot(lambda x: f1(x), x_range = [-7,7], color = BLUE))
E2 = Axes(x_range = [-9,9,2], y_range = [-2,3,1] , x_length = 4, y_length = 3).move_to([3.5,0,0])
n12 = always_redraw(lambda: MathTex('y').next_to( E2, UP, buff = 0 ).shift(0.3*LEFT+0.2*DOWN) )
n13 = always_redraw(lambda: MathTex('t').next_to( E2, RIGHT, buff = 0).shift(0.5*DOWN) )
c2 = always_redraw(lambda: E2.plot(lambda x: f2(x), x_range = [-7,7], color = YELLOW))
G0 = VGroup(E1,n10,n11,n6, c1)
G1 = VGroup(E2, n12,n9,n13, c2)
ne = Tex('\\textit{A - Amplitude}').move_to([0,3,0]).scale(1.5)
######################################################### Equação envolvendo amplitude
ne01 = MathTex('A \\cdot G(t)=').move_to([3.4,1.5,0])
ne02 = MathTex('cos(t)').next_to(ne01, RIGHT, buff = 0.7)
ne1 = VGroup(ne01,ne02)
#########################################################
# CRIAR OBJETO n14. OBJETO QUE SIMULA UMA CONTAGEM NUMÉRICA NA TELA.
######################################################### Plano que cobre a cena
retangulo = Rectangle().scale(4).set_opacity(0.9).set_color(BLACK).move_to([0,0,1])
def cobrir_cena(x):
if x ==1:
return self.play(FadeIn(retangulo))
else:
return self.play(FadeOut(retangulo))
#################################################################################
# n14 criar contador numérico
n14 = DecimalNumber(1).scale(0.7)
n14.add_updater(lambda d: d.set_value(Ac2.get_value()))
n15 = MathTex('-1\leqslant cos(t)\leqslant 1').move_to([0,0,0])
n16 = MathTex('-A\leqslant A\cdot cos(t)\leqslant A').move_to([0,0,0])
# n17 criar contador numérico
n17 = DecimalNumber(1)
n17.add_updater(lambda d: d.set_value(w2.get_value()).scale(0.5))
n18_0 = MathTex('G(\\omega \\cdot t)=cos(').move_to([3.8,1.8,0])
n18_1 = MathTex('t)').next_to(n18_0, RIGHT, buff = 0.6)
n18 = VGroup(n18_0, n18_1)
n19_0 = MathTex('\\omega').move_to([-3,3,0]).scale(2)
n19_1 = Text(' - Velocidade Angular').next_to(n19_0, RIGHT, buff = 0.2)
n19 = VGroup(n19_0,n19_1)
caux1=E1.plot(lambda x: f1(x), x_range = [0,2*PI], color = GREEN, stroke_width = 10 )
caux2=E2.plot(lambda x: f2(x), x_range = [0,(2*PI)/w2.get_value()], color = GREEN, stroke_width = 10)
n22 = MathTex('G(\\theta) = G(\\omega \\cdot t)').move_to([0,0,0])
n23 = MathTex('\\theta =\\omega \\cdot t').move_to([0,0,0])
n24 = MathTex('\\omega').move_to([-0.5,0,0])
n25 = MathTex('=').next_to(n24, RIGHT, buff = 0.2)
n26 = MathTex('\\frac{\\theta}{t}').next_to(n25, RIGHT, buff = 0.2)
n28 = MathTex('\\frac{\\bigtriangleup \\theta }{\\bigtriangleup t }').move_to(n26.get_center()+0.2*RIGHT)
n30 = MathTex('T')
n31 = MathTex('\\frac{2 \\pi}{\\bigtriangleup t}')
n32 = MathTex('\\frac{2 \\pi}{\\bigtriangleup t}')
n33 = MathTex('T = \\frac{2 \\pi}{\\omega}')
G02 = VGroup(n24,n25,n28)
G2 = VGroup(n24,n25,n32)
n34_0 = MathTex('f').scale(2)
n34_1 = Tex(' - Frequência Angular ').scale(1.5).next_to(n34_0, RIGHT, buff = 0.2)
n34 = VGroup(n34_0, n34_1)
n35_0 = Tex('N° de ciclos que').scale(1.5)
n35_1 = Tex('ocorrem em 1 segundo ').scale(1.5).next_to(n34_0, DOWN, buff = 0.2)
n35 = VGroup(n35_0, n35_1)
n36 = MathTex('f = \\frac{1}{T}')
n37 = MathTex('T = \\frac{2 \\pi}{\\omega}')
n38 = MathTex('f = \\frac{\\omega}{2 \\pi}')
n39 = MathTex('\\omega = 2 \\pi f')
ne3_0 = MathTex('\\phi').scale(2)
ne3_1 = Tex(' - Ângulo de Fase ').scale(1.5).next_to(n34_0, RIGHT, buff = 0.2)
ne3= VGroup(ne3_0, ne3_1)
n40_0 = MathTex('G(\\theta + \\phi) = cos(\\theta ')
n40_1 = MathTex(' )').next_to(n40_0, RIGHT, buff = 0.8)
n40 = VGroup(n40_0, n40_1).set_color_by_gradient([BLUE, WHITE])
# criar n41 contador
n41 = DecimalNumber(0)
n41.add_updater(lambda d: d.set_value(w1.get_value()))
n42_0 = MathTex('G(t +\\phi) = cos(t ')
n42_1 = MathTex(' )').next_to(n42_0, RIGHT, buff = 0.8)
n42 = VGroup(n42_0, n42_1).set_color_by_gradient([YELLOW, WHITE])
# criar n43 contador
n43 = DecimalNumber(0)
n43.add_updater(lambda d: d.set_value(w1.get_value()))
n44 = MathTex('\\phi')
n45 = MathTex('\\phi')
n46 = MathTex('\\phi')
n47 = MathTex('\\phi')
# criar v2 v3 v4 v5
v1_0 = Arrow([0,0,0],[-1,0,0], buff=0)
v1_1 = Arrow([0,0,0],[1,0,0], buff=0)
v1 = VGroup(v1_0, v1_1)
v2 = Arrow(E1.c2p(-0.1,-1.5,0),E1.c2p(-3,-1.5,0), buff=0)
v3 = Arrow(E1.c2p(0.1,-1.5,0),E1.c2p(3,-1.5,0), buff=0)
v4 = Arrow(E2.c2p(-0.1,-1.5,0),E2.c2p(-3,-1.5,0), buff=0)
v5 = Arrow(E2.c2p(0.1,-1.5,0),E2.c2p(3,-1.5,0), buff=0)
n48 = MathTex('G(\\omega t +\\phi) = cos(\\omega t + \\phi) ')
n51 = MathTex('A \\cdot cos(\\omega t + \\phi) ')
n52 = MathTex('g(t)=A \\cdot cos(\\omega \\cdot t + \\phi) ')
####################################################################################################
# PRODUÇÃO CENAS DINÂMICAS
####################################################################################################
# cena 16
########################################################### cena 9(atualize este código)
############################## cena 4(atualize este código)
self.add(n10)
self.add(n11)
self.add(E1)
self.add(c1)
n7.move_to([-3.5,-3,0])
self.add(n7)
n6.move_to([-1.5,2,0])
self.add(n6)
self.add(n12)
self.add(n13)
self.add(E2)
self.add(c2)
n5.move_to([3.5,-3,0])
self.add(n5)
n9.move_to([5.3,2,0])
self.add(n9)
###########################################################
G0.shift(0.5*LEFT)
G1.shift(1.5*LEFT)
#self.add(n18)
###################################################################################
ne3.move_to([0,3,0])
#self.add(ne3)
n40.move_to(n6.get_center()+0.5*DOWN).scale(0.8)
n42.move_to(n9.get_center()+0.5*DOWN+0.2*RIGHT).scale(0.8)
#self.add(n40)
#self.add(n42)
n44.move_to(E1.c2p(-2,-1.9,0))
n45.move_to(E1.c2p(2,-1.9,0))
n46.move_to(E2.c2p(-2,-1.9,0))
n47.move_to(E2.c2p(2,-1.9,0))
#self.add(n44, n45, n46, n47)
v2 = Arrow(E1.c2p(-0.1,-1.5,0),E1.c2p(-3,-1.5,0), buff=0)
v3 = Arrow(E1.c2p(0.1,-1.5,0),E1.c2p(3,-1.5,0), buff=0)
v4 = Arrow(E2.c2p(-0.1,-1.5,0),E2.c2p(-3,-1.5,0), buff=0)
v5 = Arrow(E2.c2p(0.1,-1.5,0),E2.c2p(3,-1.5,0), buff=0)
#self.add(v2,v3,v4,v5)
# n411 a n434 criar contador numérico
n411 = MathTex('+0').scale(0.8).next_to(n40_0, RIGHT, buff = 0.1)
n412 = MathTex('+2').scale(0.8).next_to(n40_0, RIGHT, buff = 0.1)
n413 = MathTex('+0').scale(0.8).next_to(n40_0, RIGHT, buff = 0.1)
n414 = MathTex('-2').scale(0.8).next_to(n40_0, RIGHT, buff = 0.1)
n431 = MathTex('+0').scale(0.8).next_to(n42_0, RIGHT, buff = 0.1)
n432 = MathTex('+2').scale(0.8).next_to(n42_0, RIGHT, buff = 0.1)
n433 = MathTex('+0').scale(0.8).next_to(n42_0, RIGHT, buff = 0.1)
n434 = MathTex('-2').scale(0.8).next_to(n42_0, RIGHT, buff = 0.1)
self.wait(3)
self.play(Write(ne3), run_time = 3)
self.wait(2)
self.play(Transform(n6, n40),FadeIn(n411), run_time =2)
self.wait(2)
self.play(Transform(n9, n42),FadeIn(n431), run_time =2)
self.wait(10)
self.play( Transform(n411,n412), Transform(n431,n432), run_time = 4)
self.play( phic1.animate.set_value(2.5),FadeIn(v2),FadeIn(n44),phic2.animate.set_value(2.5),FadeIn(v4),FadeIn(n46), run_time= 4)
self.wait(10)
self.play( Transform(n411,n413), Transform(n431,n433), run_time = 2 )
self.play( phic1.animate.set_value(0),FadeOut(v2),FadeOut(n44),phic2.animate.set_value(0),FadeOut(v4),FadeOut(n46) )
self.wait()
self.play( Transform(n411,n414), Transform(n431,n434), run_time = 2 )
self.play( phic1.animate.set_value(-2.5),FadeIn(v3),FadeIn(n45),phic2.animate.set_value(-2.5),FadeIn(v5),FadeIn(n47), run_time = 2)
self.wait(7)
g1 = VGroup(v3,v5,n45,n47,G0,G1,n5,n7,ne3,n411,n431)
self.play(FadeOut(g1))
%%manim -qm -v WARNING senoide_estatica07
class senoide_estatica07(Scene): def construct(self):
##############################################################################
# CRIAR OBJETOS MANIM
##############################################################################
Ac1 = ValueTracker(1) # rastreador da amplitude c1
w1 = ValueTracker(1)
phic1 = ValueTracker(0)
Ac2 = ValueTracker(1) # rastreador da amplitude c2
w2 = ValueTracker(1)
phic2 = ValueTracker(0)
n1 = MathTex('f(t) = A \cdot sin(\omega \cdot t)').move_to([-3,1.5,0]).set_color_by_gradient([RED, WHITE]).scale(1.2)
n2 = MathTex('g(t) = A \cdot cos(\omega \cdot t)').move_to([3.5,1.5,0]).set_color_by_gradient([RED, WHITE]).scale(1.2)
n3 = Tex('\\textit{Senoides}', color = YELLOW).move_to([-3,-0.5,0]).scale(1.5)
n4 = Tex('\\textit{Cossenoides}', color = YELLOW).move_to([3.5,-0.5,0]).scale(1.5)
n5 = Tex('\\textsc{Domínio do tempo}', opacity = 1).move_to([0,-2.5,0]).set_color_by_gradient([GRAY, WHITE])
ne4 = MathTex('F( \\theta)=sin( \\theta)').move_to([-3,1.5,0]).scale(1.2).set_color_by_gradient([BLUE, WHITE])
n6 = MathTex('G( \\theta)=cos( \\theta)').move_to([3,1.5,0]).scale(1.2).set_color_by_gradient([BLUE, WHITE])
n7 = Tex('\\textsc{Domínio do Ângulo}').move_to([0,-1,0]).set_color_by_gradient([GRAY, WHITE])
n8 = Tex('\\textit{Mudar Domínio}').move_to([0,-2,0]).scale(1.5)
n9 = MathTex('G(t)=cos(t)').move_to([0,0,0]).set_color_by_gradient([YELLOW, WHITE]).scale(1.2)
def f1(x):
return Ac1.get_value()*np.cos(w1.get_value()*x + phic1.get_value())
def f2(x):
return Ac2.get_value()*np.cos(w2.get_value()*x + phic2.get_value())
E1 = Axes(x_range = [-9,9,2], y_range = [-2,3,1] , x_length = 4, y_length = 3).move_to([-3.5,0,0])
n10 = MathTex('y').next_to( E1, UP, buff = 0 ).shift(0.3*LEFT+0.2*DOWN)
n11 = MathTex('\\theta').next_to( E1, RIGHT, buff = 0).shift(0.5*DOWN)
c1 = always_redraw(lambda: E1.plot(lambda x: f1(x), x_range = [-7,7], color = YELLOW))
E2 = Axes(x_range = [-9,9,2], y_range = [-2,3,1] , x_length = 4, y_length = 3).move_to([3.5,0,0])
n12 = always_redraw(lambda: MathTex('y').next_to( E2, UP, buff = 0 ).shift(0.3*LEFT+0.2*DOWN) )
n13 = always_redraw(lambda: MathTex('t').next_to( E2, RIGHT, buff = 0).shift(0.5*DOWN) )
c2 = always_redraw(lambda: E2.plot(lambda x: f2(x), x_range = [-7,7], color = YELLOW))
G0 = VGroup(E1,n10,n11,n6, c1)
G1 = VGroup(E2, n12,n9,n13, c2)
ne = Tex('\\textit{A - Amplitude}').move_to([0,3,0]).scale(1.5)
######################################################### Equação envolvendo amplitude
ne01 = MathTex('A \\cdot G(t)=').move_to([3.4,1.5,0])
ne02 = MathTex('cos(t)').next_to(ne01, RIGHT, buff = 0.7)
ne1 = VGroup(ne01,ne02)
#########################################################
# CRIAR OBJETO n14. OBJETO QUE SIMULA UMA CONTAGEM NUMÉRICA NA TELA.
######################################################### Plano que cobre a cena
retangulo = Rectangle().scale(4).set_opacity(0.7).set_color(BLACK).move_to([0,0,1])
def cobrir_cena(x):
if x ==1:
return self.play(FadeIn(retangulo))
else:
return self.play(FadeOut(retangulo))
#################################################################################
# n14 criar contador numérico
n14 = DecimalNumber(1).scale(0.7)
n14.add_updater(lambda d: d.set_value(Ac2.get_value()))
n15 = MathTex('-1\leqslant cos(t)\leqslant 1').move_to([0,0,0])
n16 = MathTex('-A\leqslant A\cdot cos(t)\leqslant A').move_to([0,0,0])
# n17 criar contador numérico
n17 = DecimalNumber(1)
n17.add_updater(lambda d: d.set_value(w2.get_value()).scale(0.5))
n18_0 = MathTex('G(\\omega \\cdot t)=cos(').move_to([3.8,1.8,0])
n18_1 = MathTex('t)').next_to(n18_0, RIGHT, buff = 0.6)
n18 = VGroup(n18_0, n18_1)
n19_0 = MathTex('\\omega').move_to([-3,3,0]).scale(2)
n19_1 = Text(' - Velocidade Angular').next_to(n19_0, RIGHT, buff = 0.2)
n19 = VGroup(n19_0,n19_1)
caux1=E1.plot(lambda x: f1(x), x_range = [0,2*PI], color = GREEN, stroke_width = 10 )
caux2=E2.plot(lambda x: f2(x), x_range = [0,(2*PI)/w2.get_value()], color = GREEN, stroke_width = 10)
n22 = MathTex('G(\\theta) = G(\\omega \\cdot t)').move_to([0,0,0])
n23 = MathTex('\\theta =\\omega \\cdot t').move_to([0,0,0])
n24 = MathTex('\\omega').move_to([-0.5,0,0])
n25 = MathTex('=').next_to(n24, RIGHT, buff = 0.2)
n26 = MathTex('\\frac{\\theta}{t}').next_to(n25, RIGHT, buff = 0.2)
n28 = MathTex('\\frac{\\bigtriangleup \\theta }{\\bigtriangleup t }').move_to(n26.get_center()+0.2*RIGHT)
n30 = MathTex('T')
n31 = MathTex('\\frac{2 \\pi}{\\bigtriangleup t}')
n32 = MathTex('\\frac{2 \\pi}{\\bigtriangleup t}')
n33 = MathTex('T = \\frac{2 \\pi}{\\omega}')
G02 = VGroup(n24,n25,n28)
G2 = VGroup(n24,n25,n32)
n34_0 = MathTex('f').scale(2)
n34_1 = Tex(' - Frequência Angular ').scale(1.5).next_to(n34_0, RIGHT, buff = 0.2)
n34 = VGroup(n34_0, n34_1)
n35_0 = Tex('N° de ciclos que').scale(1.5)
n35_1 = Tex('ocorrem em 1 segundo ').scale(1.5).next_to(n34_0, DOWN, buff = 0.2)
n35 = VGroup(n35_0, n35_1)
n36 = MathTex('f = \\frac{1}{T}')
n37 = MathTex('T = \\frac{2 \\pi}{\\omega}')
n38 = MathTex('f = \\frac{\\omega}{2 \\pi}')
n39 = MathTex('\\omega = 2 \\pi f')
ne3_0 = MathTex('\\phi').scale(2)
ne3_1 = Tex(' - Ângulo de Fase ').scale(1.5).next_to(n34_0, RIGHT, buff = 0.2)
ne3= VGroup(ne3_0, ne3_1)
n40_0 = MathTex('G(\\theta + \\phi) = cos(\\theta ')
n40_1 = MathTex(' )').next_to(n40_0, RIGHT, buff = 0.8)
n40 = VGroup(n40_0, n40_1).set_color_by_gradient([BLUE, WHITE])
# criar n41 contador
n41 = DecimalNumber(0)
n41.add_updater(lambda d: d.set_value(w1.get_value()))
n42_0 = MathTex('G(t +\\phi) = cos(t')
n42_1 = MathTex('+\\phi )').next_to(n42_0, RIGHT, buff = 0)
n42 = VGroup(n42_0, n42_1).set_color_by_gradient([YELLOW, WHITE])
# criar n43 contador
n43 = DecimalNumber(0)
n43.add_updater(lambda d: d.set_value(w1.get_value()))
n44 = MathTex('\\phi')
n45 = MathTex('\\phi')
n46 = MathTex('\\phi')
n47 = MathTex('\\phi')
# criar v2 v3 v4 v5
v1_0 = Arrow([0,0,0],[-1,0,0], buff=0)
v1_1 = Arrow([0,0,0],[1,0,0], buff=0)
v1 = VGroup(v1_0, v1_1)
v2 = Arrow(E1.c2p(-0.1,-1.5,0),E1.c2p(-3,-1.5,0), buff=0)
v3 = Arrow(E1.c2p(0.1,-1.5,0),E1.c2p(3,-1.5,0), buff=0)
v4 = Arrow(E2.c2p(-0.1,-1.5,0),E2.c2p(-3,-1.5,0), buff=0)
v5 = Arrow(E2.c2p(0.1,-1.5,0),E2.c2p(3,-1.5,0), buff=0)
n48 = MathTex('G(\\omega t +\\phi) = cos(\\omega t + \\phi) ').set_color_by_gradient([YELLOW, RED])
n51 = MathTex('A \\cdot cos(\\omega t + \\phi) ').set_color_by_gradient([YELLOW, RED])
n52 = MathTex('g(t)=A \\cdot cos(\\omega \\cdot t + \\phi) ').set_color_by_gradient([RED, WHITE])
####################################################################################################
# PRODUÇÃO CENAS DINÂMICAS
####################################################################################################
#cena 17
n6.move_to([-1.5,1.5,0])
G0.move_to([0,0,0]).scale(1.5)
G1.scale(1.5)
n9.move_to([1.5,2,0])
#self.add(G0)
n7.move_to([0,-3,0])
#self.add(n7)
n5.move_to([0,-3,0])
#self.add(n5)
n13.move_to(n11)
#self.add(n13)
#self.add(n9)
n42.move_to([2.4,2,0]).scale(1.5)
#self.add(n42)
n48.move_to([3,2,0]).scale(1.3)
#self.add(n48)
n51.move_to([1.8,2,0]).scale(1.4)
#self.add(n51)
n51.move_to([2,2,0]).scale(1.4)
#self.add(n51)
n52.move_to([2.8,2,0]).scale(1.5)
#self.add(n52)
g1 = VGroup(E1, n10,n11)
self.play(DrawBorderThenFill(g1), run_time =3)
self.play(Write(n6), run_time = 3)
c1_0 = c1.copy().set_color(BLUE)
self.play(Write(c1_0), run_time = 3)
self.play(Write(n7), run_time = 3)
self.play(Transform(n7, n5),Transform(n11, n13),Transform(n6, n9),FadeOut(c1_0),FadeIn(c1), run_time = 2)
self.wait()
self.play(Transform(n6, n42), phic1.animate.set_value(1.5), run_time = 2)
self.wait()
self.play(Transform(n6, n48), w1.animate.set_value(1.5), run_time = 2)
self.wait()
self.play(Transform(n6, n51), Ac1.animate.set_value(2), run_time = 3)
self.wait()
self.play(Transform(n6, n52), run_time = 3)
self.wait(2)
g2 = VGroup(g1,n6,c1,n7,n11)
self.play(Unwrite(g2), run_time = 3)
self.wait()