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R9442/notebooks/RLC_source.py
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RLC_source.py
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import sys
import plotly.graph_objects as go
from ipywidgets import widgets
from IPython.display import display, Image
from plotly.subplots import make_subplots
from ipywidgets import interact, interactive, fixed, interact_manual
import ipywidgets as widgets
import math
import numpy as np
from IPython.display import Video
from matplotlib.pylab import *
from mpl_toolkits.axes_grid1 import host_subplot
import matplotlib.animation as animation
import matplotlib.image as mpimg
import matplotlib.pyplot as plt
from matplotlib import animation, rc
from IPython.display import HTML
def plot_func_1(R, C):
V=1
print(' R = {0:.2f} M\u03A9 \n C = {0:.2f} \u03BCF'.format(R, C))
print('\n')
taw = R*C
t = np.linspace(0, 40, num=200)
V_c = V*(1-np.exp(-t/(taw)))
I_c = (V/R)*np.exp(-t/(taw))
fig, ax = plt.subplots(3,2)
ax[0,0].imshow(mpimg.imread('../static/img/capacitor_circuit_charge.png'))
ax[1,0].plot(t, V_c, linewidth=2, color='r')
ax[2,0].plot(t, I_c, linewidth=2, color='r')
ax[0,0].set_title('Charging a capacitor :'.format(R*C))
ax[1,0].set_title('Capacitor Voltage vs Time (\u03C4 = {0:.2f} [s])'.format(R*C))
ax[1,0].set_ylabel('V_c [V]')
ax[2,0].set_title('Capacitor Current vs Time (\u03C4 = {0:.2f} [s])'.format(R*C))
ax[2,0].set_ylabel('I_c [A]')
#ax[0].set_xlabel('time [s]')
ax[2,0].set_xlabel('time [s]')
ax[0,0].grid(False)
ax[1,0].grid(True)
ax[2,0].grid(True)
ax[0,0].axis('off')
V_c_ = V*np.exp(-t/(taw))
I_c_ = -(V/R)*np.exp(-t/(taw))
ax[0,1].imshow(mpimg.imread('../static/img/capacitor_circuit_discharge.png'))
ax[1,1].plot(t, V_c_, linewidth=2)
ax[2,1].plot(t, I_c_, linewidth=2)
ax[0,1].set_title('Discharging a capacitor :'.format(R*C))
ax[1,1].set_title('Capacitor Voltage vs Time (\u03C4 = {0:.2f} [s])'.format(R*C))
ax[1,1].set_ylabel('V_c [V]')
ax[2,1].set_title('Capacitor Current vs Time (\u03C4 = {0:.2f} [s])'.format(R*C))
ax[2,1].set_ylabel('I_c [A]')
#ax[0].set_xlabel('time [s]')
ax[0,1].grid(False)
ax[2,1].set_xlabel('time [s]')
ax[1,1].grid(True)
ax[2,1].grid(True)
ax[0,1].axis('off')
fig.tight_layout(pad=-40, w_pad=10, h_pad=3)
def animation_overdamped():
A = 1
B = 1
L = 4
C = 1
R = np.sqrt(4*L/C) + 1
m1 = -R/(2* L) + math.sqrt(R**2 - 4*L/C)/(2*L)
m2 = -R/(2* L) - math.sqrt(R**2 - 4*L/C)/(2*L)
# case 1 : overdamped
t = np.linspace(0, 20, 100)
y = A*np.exp(m1*t) + B*np.exp(m2*t)
fig, ax = plt.subplots()
line, = ax.plot(t, y, color='k')
plt.xlabel('time (t)')
plt.ylabel('current (A)')
plt.title('Overdamped Case: Current vs. Time')
def update(num, t, y, line):
line.set_data(t[:num], y[:num])
line.axes.axis([0, 20, 0, 2])
return line,
ani = animation.FuncAnimation(fig, update, len(t), fargs=[t, y, line],
interval=25, blit=True)
return ani
def animation_critically_damped():
A = 1
B = 1
L = 4
C = 1
R = np.sqrt(4*L/C)
m1 = -R/(2* L) + math.sqrt(R**2 - 4*L/C)/(2*L)
m2 = -R/(2* L) - math.sqrt(R**2 - 4*L/C)/(2*L)
# case 1 : overdamped
t = np.linspace(0, 20, 100)
y = (A+B*t)*np.exp(-R*t/(2*L))
fig, ax = plt.subplots()
line, = ax.plot(t, y, color='k')
plt.xlabel('time (t)')
plt.ylabel('current (A)')
plt.title('Critically Damped Case: Current vs. Time')
def update(num, t, y, line):
line.set_data(t[:num], y[:num])
line.axes.axis([0, 20, 0, 2])
return line,
ani = animation.FuncAnimation(fig, update, len(t), fargs=[t, y, line],
interval=25, blit=True)
return ani
def animation_under_damped():
A = 1
B = 1
L = 1
C = 1
R = sqrt(4*L/C) - 1.5
# case 1 : overdamped
t = np.linspace(0, 20, 100)
omega = sqrt(1/(L*C)-R**2/(4*L**2))
y = np.exp(-R/(2*L)*t)*(A*cos(omega*t) + B*sin(omega*t))
fig, ax = plt.subplots()
line, = ax.plot(t, y, color='k')
plt.xlabel('time (t)')
plt.ylabel('current (A)')
plt.title('Under-Damped Case: Current vs. Time')
def update(num, t, y, line):
line.set_data(t[:num], y[:num])
line.axes.axis([0, 20, -2, 2])
return line,
ani = animation.FuncAnimation(fig, update, len(t), fargs=[t, y, line],
interval=25, blit=True)
return ani
def animation_oscillator():
global x
global i
global yp1
global yv1
global yp1_
global yv1_
global yp1__
global yv1__
global t
global im
global ims
global im_2
global ims_2
img1=mpimg.imread('../static/img/schemdraw_LC_1.png')
img2=mpimg.imread('../static/img/schemdraw_LC_5.png')
img3=mpimg.imread('../static/img/schemdraw_LC_2.png')
img4=mpimg.imread('../static/img/schemdraw_LC_6.png')
img5=mpimg.imread('../static/img/schemdraw_LC_3.png')
img6=mpimg.imread('../static/img/schemdraw_LC_7.png')
img7=mpimg.imread('../static/img/schemdraw_LC_4.png')
img8=mpimg.imread('../static/img/schemdraw_LC_8.png')
img1_2=mpimg.imread('../static/img/ms_1_color.png')
img2_2=mpimg.imread('../static/img/ms_5_color_arrow.png')
img3_2=mpimg.imread('../static/img/ms_2_color_arrow.png')
img4_2=mpimg.imread('../static/img/ms_6_color_arrow.png')
img5_2=mpimg.imread('../static/img/ms_3_color.png')
img6_2=mpimg.imread('../static/img/ms_7_color_arrow.png')
img7_2=mpimg.imread('../static/img/ms_4_color_arrow.png')
img8_2=mpimg.imread('../static/img/ms_8_color_arrow.png')
# Sent for figure
font = {'size' : 20}
matplotlib.rc('font', **font)
# Setup figure and subplots
f0 = figure(num = 0, figsize = (32, 32))#, dpi = 100)
f0.suptitle("LC oscillator - analogy with mechanical oscillator", fontsize=28)
ax01 = subplot2grid((3, 2), (0, 0))
ax01.axis('off')
#ax02 = subplot2grid((2, 2), (0, 1))
ax03 = subplot2grid((3, 2), (1, 0))
ax04 = ax03.twinx()
ax05 = subplot2grid((3, 2), (2, 0))
ax06 = ax05.twinx()
ax06.axis('off')
ax01_2 = subplot2grid((3, 2), (0, 1))
ax01_2.axis('off')
ax03_2 = subplot2grid((3, 2), (1, 1))
ax04_2 = ax03_2.twinx()
ax07 = subplot2grid((3, 2), (2, 1))
ax08 = ax07.twinx()
ax08.axis('off')
# Set titles of subplots
ax01.set_title('LC-circuit')
ax01_2.set_title('Mass Spring Oscilation')
#ax02.set_title('Velocity vs Time')
ax03.set_title('Charge and Current vs Time')
ax03_2.set_title('Position and Velocity vs Time')
ax05.set_title('Energy vs Time')
omega=2*math.pi/10
phi=0
A=1
# set y-limits
ax03.set_ylim(-A-1,A+1)
ax04.set_ylim(-A*omega-1,A*omega+1)
ax05.set_ylim(0,100)
ax06.set_ylim(0,100)
ax07.set_ylim(0,100)
ax08.set_ylim(0,100)
ax03_2.set_ylim(-A-1,A+1)
ax04_2.set_ylim(-A*omega-1,A*omega+1)
# sex x-limits
ax03.set_xlim(0,10)
ax04.set_xlim(0,10)
ax05.set_xlim(0,10)
ax06.set_xlim(0,10)
ax07.set_xlim(0,10)
ax08.set_xlim(0,10)
ax03_2.set_xlim(0,10)
ax04_2.set_xlim(0,10)
# Turn on grids
ax03.grid(True)
ax03_2.grid(True)
ax05.grid(True)
ax07.grid(True)
# set label names
ax03.set_xlabel("t")
ax03.set_ylabel("charge")
ax04.set_ylabel("current")
ax03_2.set_xlabel("t")
ax03_2.set_ylabel("position")
ax04_2.set_ylabel("velocity")
ax05.set_xlabel("t")
ax05.set_ylabel("Total energy percent")
ax07.set_xlabel("t")
ax07.set_ylabel("Total energy percent")
# Data Placeholders
yp1=zeros(0)
yv1=zeros(0)
yp1_=zeros(0)
yv1_=zeros(0)
yp1__=zeros(0)
yv1__=zeros(0)
t=zeros(0)
# set plots
im = ax01.imshow(img1, animated=True)
im_2 = ax01_2.imshow(img1_2, animated=True)
p031, = ax03.plot(t,yp1,'m-', label="charge")
p032, = ax04.plot(t,yv1,'k-', label="current")
p031_2, = ax03_2.plot(t,yp1,'m-', label="position")
p032_2, = ax04_2.plot(t,yv1,'k-', label="velocity")
p051, = ax05.plot(t,yp1_,'b-', linewidth=5, label="electrical energy")
p052, = ax06.plot(t,yv1_,'r-', linewidth=5, label="magnetic energy")
p071, = ax07.plot(t,yp1__,'b-', linewidth=5, label="potential energy")
p072, = ax08.plot(t,yv1__,'r-', linewidth=5, label="kinetic energy")
# set lagends
ax03.legend([p031,p032], [p031.get_label(),p032.get_label()])
ax03_2.legend([p031_2,p032_2], [p031_2.get_label(),p032_2.get_label()])
ax05.legend([p051,p052], [p051.get_label(),p052.get_label()])
ax07.legend([p071,p072], [p071.get_label(),p072.get_label()])
# Data Update
xmin = 0.0
xmax = 10.0
x = 0.0
i=0
ims=[]
ims_2=[]
def updateData(self):
global x
global i
global yp1
global yv1
global yp1_
global yv1_
global yp1__
global yv1__
global t
global im
global ims
global im_2
global ims_2
tmpp1 = -A*cos(omega*x+phi)
tmpv1 = A*omega*sin(omega*x+phi)
yp1=append(yp1,tmpp1)
yv1=append(yv1,tmpv1)
t=append(t,x)
AA=10
k = 2*100/(10/2)**2
tmpp1_ = 1/2*k*(x-10/2)**2
tmpv1_ = 100 - tmpp1_
yp1_=append(yp1_,tmpp1_)
yv1_=append(yv1_,tmpv1_)
AA=10
k = 2*100/(10/2)**2
tmpp1__ = 1/2*k*(x-10/2)**2
tmpv1__ = 100 - tmpp1__
yp1__ = append(yp1__,tmpp1__)
yv1__ = append(yv1__,tmpv1__)
x += 10/8
if i%1==0 or i==0:
if i==0:
im = []
im = ax01.imshow(img1, animated=True)
ims.append([im])
im_2 = []
im_2 = ax01_2.imshow(img1_2, animated=True)
ims_2.append([im_2])
elif i==1:
im = ax01.cla()
ax01.axis('off')
im = ax01.imshow(img2, animated=True)
ims.append([im])
im_2 = []
im_2 = ax01_2.imshow(img2_2, animated=True)
ims_2.append([im_2])
elif i==2:
im = ax01.cla()
ax01.axis('off')
im = ax01.imshow(img3, animated=True)
ims.append([im])
im_2 = []
im_2 = ax01_2.imshow(img3_2, animated=True)
ims_2.append([im_2])
elif i==3:
im = ax01.cla()
ax01.axis('off')
im = ax01.imshow(img4, animated=True)
ims.append([im])
im_2 = []
im_2 = ax01_2.imshow(img4_2, animated=True)
ims_2.append([im_2])
elif i==4:
im = ax01.cla()
ax01.axis('off')
im = ax01.imshow(img5, animated=True)
ims.append([im])
im_2 = []
im_2 = ax01_2.imshow(img5_2, animated=True)
ims_2.append([im_2])
elif i==5:
im = ax01.cla()
ax01.axis('off')
im = ax01.imshow(img6, animated=True)
ims.append([im])
im_2 = []
im_2 = ax01_2.imshow(img6_2, animated=True)
ims_2.append([im_2])
elif i==6:
im = ax01.cla()
ax01.axis('off')
im = ax01.imshow(img7, animated=True)
ims.append([im])
im_2 = []
im_2 = ax01_2.imshow(img7_2, animated=True)
ims_2.append([im_2])
elif i==7:
im = ax01.cla()
ax01.axis('off')
im = ax01.imshow(img8, animated=True)
ims.append([im])
im_2 = []
im_2 = ax01_2.imshow(img8_2, animated=True)
ims_2.append([im_2])
else:
im = []
ims.append([im])
im_2 = []
ims_2.append([im_2])
i +=1
p031.set_data(t,yp1)
p032.set_data(t,yv1)
p031_2.set_data(t,yp1)
p032_2.set_data(t,yv1)
p051.set_data(t,yp1_)
p052.set_data(t,yv1_)
p071.set_data(t,yp1__)
p072.set_data(t,yv1__)
return ims, p031, p032, p031_2, p032_2, p051, p052, p071, p072
tight_layout(pad=8, w_pad=5, h_pad=3)
# interval: draw new frame every 'interval' ms
# frames: number of frames to draw
ani = animation.FuncAnimation(f0, updateData, blit=False, frames=8, interval=20, repeat=True)
return ani
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