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#!/usr/bin/env python

from argparse import ArgumentParser

import numpy as np

import matplotlib.pyplot as plt

arg_parser = ArgumentParser(description='plots damped pendulum amplitude')

arg_parser.add_argument('--mu', type=float, default=0.2,

help='damping coefficient')

arg_parser.add_argument('--alpha', type=float, default=0.8,

help='alpha factor for envelope curves')

arg_parser.add_argument('--width', type=float, default=1.0,

help='line width for envelope curves')

arg_parser.add_argument('file', nargs='?', help='output file name')

options = arg_parser.parse_args()

eq = (r'$\frac{d^2 \theta}{dt^2} = - \frac{g}{l} \theta ' +

r'- \mu \frac{d\theta}{dt}$')

x = np.linspace(0.0, 20.0, 500)

y = np.exp(-options.mu*x)*np.cos(2.0*np.pi*x)

y_plus = np.exp(-options.mu*x)

y_min = -np.exp(-options.mu*x)

plt.plot(x, y)

plt.plot(x, y_plus, ':', alpha=options.alpha, color='red',

linewidth=options.width)

plt.plot(x, y_min, ':', alpha=options.alpha, color='red',

linewidth=options.width)

plt.xlabel(r'$t$', fontsize=14)

plt.ylabel(r'$\theta(t)$', fontsize=14)

plt.title('Damped pendulum')

plt.text(10.0, 0.65, eq, fontsize=18)

if options.file:

plt.savefig(options.file)

else:

plt.show()