# Forced damped driven pendulum (Scripts) 1.0

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• Last update: 6 years ago
• Price: Free |
• Operating system: Linux, Mac OS X, Win All, BSD, Solaris
• Publisher: Adam Wyatt (10 other programs)
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## Forced damped driven pendulum (Scripts) Publisher's description

### This simulink model simulates the damped driven pendulum, showing it's chaotic motion.

This simulink model simulates the damped driven pendulum, showing it's chaotic motion.
theta = angle of pendulum
omega = (d/dt)theta = angular velocity
Gamma(t) = gcos(phi) = Force
omega_d = (d/dt) phi
Gamma(t) = (d/dt)omega + omega/Q + sin(theta)

Play with the initial conditions (omega_0, theta_0, phi_0 = omega(t=0), theta(t=0), phi(t=0)) and the system parameters (g, Q, omega_d) and the solver parameters/method.

Chaos can be seen for Q=2, omega_d=w/3.

The program outputs to Matlab time, theta(time) & omega(time).

Plot the phase space via:
plot(mod(theta+pi, 2*pi)-pi, omega, '.');

Plot the Poincare sections using:
t_P = (0:2*pi/omega_d:max(time))';
plot(mod(spline(time, theta+pi, t_P), 2*pi)-pi, spline(time, omega, t_P), '.');

System is described in:
"Fractal basin boundaries and intermittency in the driven damped pendulum"
E. G. Gwinn and R. M. Westervelt
PRA 33(6):4143 (1986)

#### System Requirements:

MATLAB 7.4 (R2007a)
Program Release Status: New Release
Program Install Support: Install and Uninstall

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