There is physics everywhere, including on the playground. At the College Mathematics Journal, physicists have tackled the age old question: what's the best way to swing a playground swing?
The physicists in question consider two kinds of swinging: standing and seated. A standing rider pumps the swing by crouching down at the high point of the swing, and standing up at the low point. A sitting rider swings their legs out at the high point, and draws them in as it swings down. So which is better?
Our main conclusion is that seated pumping is the better strategy at low amplitudes, but above certain amplitude standing is more effective. This will come as no surprise to experienced swing riders, but the argument provides a nice example of how modeling and quantitative analysis with differential equations can lead to a deeper understand of a familiar system.
In other words, seating swinging is the way to go, unless you want to go really high.
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