WOLFRAM|DEMONSTRATIONS PROJECT

Motion of a Simple Pendulum with Damping

​
step
pendulum length
angular velocity
damping
This Demonstration shows the motion of a pendulum obeying a classical pendulum differential equation with damping proportional to its angular velocity.
The visualization contains an approximate solution to the simple pendulum equation (with damping)
∂
t,t
θ=-ksin(θ)-α
∂
t
θ
, where
θ
is the pendulum angle,
t
is time,
k
is a length parameter, and
α
is a damping factor. The diagram on the left is a phase portrait of the system, where the horizontal axis is the angle of the pendulum and the vertical axis is the angular velocity.