Pendulum with Rotating Pivot

start/reset

mass of bob m

1

bob start speed

''

θ

0

25°

damping coefficient μ

0.1

crank radius R

0.25

crank speed Ω

10

randomize parameters

This Demonstration shows a special case of the damped and driven double pendulum. The suspension point (pivot) of a pendulum of length

L

and bob mass

m

is attached to a crank of length

R

rotating at a constant angular speed

Ω

. The damping coefficient of the system is

μ

. To limit the number of parameters, we take

L=1

and the starting position of the bob at

θ

0

=15°

. Then the equation of motion is

Lmθ''(t)+Lμθ'(t)+mgsin(θ(t))+mR

2

Ω

sin(tΩ-θ(t))0

. The animation traces the movement of the pendulum bob.