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

1 Answer
Sep 29, 2014

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:


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

I hope that this was helpful.