Regardless of where you are from, you’ve probably had this childhood experience of pumping a swing: where you flatten your body as you go forward, and curl up as you go back. This action causes you to swing higher and higher. Until recently, I’ve never considered the physics of how this works, but it’s an interesting concept that I think is the answer to a question that has probably frequented a lot of people’s heads.
One explanation to this motion is the mechanisms of a parametric oscillator.
As the most basic form of a pendulum, here is a visual representation of the oscillation of a simple damped pendulum:
When you ride a swing without pumping your body, the motion of the swing follows the mechanisms of a simple damped pendulum. You slowly stop getting higher and you stop. However, when you pump, you’re changing the center of mass within your body, modulating the length of the swing’s string.
A demonstration of this can be found on youtube: parametric oscillator pendulum
By decreasing the length of the string as it reaches the top, and increasing it as it reaches the bottom, there is an external drive added to the equation based on time. This additional equation is what makes the motion of pumping a swing a parametric oscillation.
Sources :
https://aip.scitation.org/doi/10.1063/1.4904465
https://www.youtube.com/watch?v=gY3ymZC6t9M&ab_channel=WescottDesignServices
https://www.youtube.com/watch?v=MbWhKFIayp4&t=105s&ab_channel=casewm
