How does an infinite geometric series apply to being pushed on a swing?

Question

Scarlett Allison · Accepted Answer

If you wish to find the total horizontal distance traveled by you on a swing after a big initial push assuming that the amplitude of each swing decreases at a fixed rate. We can think of the total distance as the sum of a geometric series.

Assume that the initial push gives you a 3 m swing and that a swing is #6/7# of its previous swing. The total horizontal distance can be expressed as the geometric series:

#3+3(6/7)+3(6/7)^2+3(6/7)^3+cdots=3/{1-6/7}=21#

In theory, the total horizontal distance is #21# m.

I hope that this was helpful.

Cameron Alexander · Answer

undefined An infinite geometric series can be used to model the motion of a swing. When you're pushed on a swing, your motion follows a repetitive pattern, much like the terms of a geometric series. As you swing back and forth, the distance you travel decreases with each swing, forming a geometric sequence. The total distance you travel over time can be represented by the sum of an infinite geometric series.