LRC network simulation

This script simulates a classical LRC electrical circuit consisting of an inductor, a resistor and a capacitor. An step voltage is applied to the input, and the voltage across the capacitor exhibits oscillatory behavior.

from pylab import figure, plot, show, grid, ion, legend,xlabel,ylabel
import scipy.integrate
import time
import numpy

def f_LC(t, state, arg1):
    charge, field = state
    L, C, R = arg1
    I_L = field / L
    U_C = charge / C
    # Step function:
    if (t > 1.0):
      Vin = 1.0
    else:
      Vin = 0.0
    U_R = R * I_L # Ohms law
    dfield = Vin - U_C - U_R # Calculate voltage across coil
    rates = [I_L, dfield]
    return rates

def main():
    initial_state = [0.0, 0.0] # Initial charge and field
    L = 0.1 # Henry
    C = 0.1 # Farad
    R = 0.1 # Ohm
    t0 = 0.0
    t1 = 10.0 # Seconds
    dt = 0.01 # Seconds

    r = scipy.integrate.ode(f_LC)
    r.set_integrator('zvode', method='bdf', with_jacobian=False)
    r.set_f_params([L, C, R])
    r.set_initial_value(initial_state, t0)

    t = list()
    charge = list()
    while r.successful() and r.t < t1:
        r.integrate(r.t+dt)
        t.append(r.t)
        charge.append(r.y[0])

    figure()
    U_C = numpy.array(charge) / C
    plot(t, U_C, 'o-',label='voltage across capacitor [V]')
    legend()
    grid(True)
    xlabel('time [s]')
    ylabel('Electrical potential [V]')
    show()

if __name__ == '__main__':
    main()