View source for CompSciHW9

Introduction to Scientific Computing, HW 9.  Due Friday, Apr. 15, 2016.

<pre>
1) Use the van der Pol oscillator class to simulate 60 second (6000 steps) trajectories with 3 initial conditions, 
  x, v = [4, 3], [4, 4], and [4, 5]
  Here, v = dot x = dx/dt

2) Add a method to calculate the energy of a harmonic oscillator,
  E(x, v) = (x^2 + v^2)/2

3) Plot E(t) for all 3 simulations on the same axes.  Remember to scale t = arange(6000)*dt.

4) Is there a pattern that would let you know when the oscillator is near the steady-state?
</pre>

Remember, we built the van der Pol integrator on [[CompSciWeek13]].  The complete code is below,

<source lang="python">
#!/usr/bin/env python
 
import sys
from numpy import *
from numpy.random import standard_normal
norm = standard_normal


class State:
    def __init__(self, x, v, mu, dt):
        assert x.shape == v.shape
        self.mu = mu
        self.dt = dt
        self.x = x
        self.v = v
#
    def step(self, N=1):
        for i in xrange(N):
           self.v += (self.mu*(1.0-self.x**2)*self.v - self.x)*self.dt
           self.x += self.v*self.dt
    def __str__(self):
        s = ""
        for x,v in zip(self.x, self.v):
            s += " %f %f"%(x, v)
        return s


def main(argv):
    assert len(argv) == 2, "Usage: %s <mu>"%argv[0]
    mu = float(argv[1])
    print mu
    dt = 0.01
    st = State(array([2.0]), array([0.0]), mu, dt)
    st.step(10)
    print st
 
if __name__=="__main__":
    main(sys.argv)
</source>