Simple Pendulum 

Function: calc[Pendulum] - animates the motion of a simple pendulum 

Calling Sequence:  

Pendulum(L, theta[0], r, options) 

Parameters: 

L   - length of the pendulum 

theta[0] - initial angular position in degrees 

r   - damping coefficient 

options - plot options for the display command 

Description: 

  • Pendulum creates an animation of the motion of a simple pendulum. The angular position theta is controlled by the numerical solution of the differential equation
 

diff(theta(t), t, t)r diff(theta(t), t)`/`(`*`(g), `*`(L)) `*`(sin, `*`(theta(t))) = 0 

which describes the motion of the pendulum. The initial angular velocity is assumed zero 

Examples: 

> restart: with(calc):
 

> Pendulum(5,60,0.2,scaling=constrained,axes=normal,tickmarks=[4,4]);
 

 

 

 

`+`(diff(diff(theta(t), t), t), `*`(.2, `*`(diff(theta(t), t))), `*`(1.960000000, `*`(sin(theta(t))))) = 0
Pseudoperiod
T = 5.057414084
Plot_2d