Pendulum with Varying Length or How to Improve Your Next Swing Ride

animation

fast

medium

slow

swinging

initial angular position

1.31

initial angular speed

0

crouching

amplitude

0.75

frequency

6.004

show trace

periods
swinging θ(t)	7.1	s
crouching L(t)	1.046	s
ratio swing/crouch	6.78

Moving up and down on the seat of the swing influences its motion. This Demonstration simulates a swing as a child crouches down and straightens up from the seat in an oscillating manner, thus mimicking a pendulum with cyclically varying length.

Remember from childhood that to make a swing move higher and higher, you must alternate between crouching and straightening up. The best result is obtained when this is done with a period that is approximately half the period of the swing.

Using the sliders and looking at the curves, you can get ever-increasing swing length, a gracefully periodic motion, or a chaotic movement. Have fun!