Damped Swing Pendulum

frame

time

board x

0.7

board y

0.25

board z

0.05

height from ground

0.7

rod diameter

0.05

rod length

1

initial velocity

1

initial position

0

damping

1

5

1

10

1

15

1

20

This Demonstration solves the differential equation for a damped swing pendulum,

φ''(t)+kφ'(t)+

g

l

sinφ(t)=0

. Interestingly, starting from a vertical position with zero initial velocity, Mathematica starts the motion on its own (for a small-enough damping constant) because of numerical roundoff errors, somewhat similar to effects which occur in chaotic dynamics.