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## Forced damped driven pendulum

version 1.0.0.0 (8.35 KB) by Adam Wyatt

### Adam Wyatt (view profile)

A forced damped driven pendulum exhibits chaotic motion.

Updated 23 Jul 2007

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)

### Adam Wyatt (view profile)

Great. Could you send me the haddock - I'm not interested in the cod, possibly the pangasius.

alaa taha

good job
can you help me by take me only the cod of
forced damped driven pendulum exhibits chaotic motion to use it in my research
(i need the general cod not the simulink cod)

##### MATLAB Release Compatibility
Created with R2007a
Compatible with any release
##### Platform Compatibility
Windows macOS Linux