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

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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!
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