Question

Chapter 15 1. By what percent does the period of a simple pendulum change if you double its (a) amplitude; (b) mass; (c) length?

Period of a simple pendulum, T = 2(pi) sqrt(l/g)

Answer 1

The period of simple pendulum is given by

Part-a

When the amplitude is doubled the time period remains same, becaue time period of simple pendulum depends only on the length of the string

Hence the % change in time period is zero.

Part-b

When mass is doubled

again time periond remains same and the percentage change is zero.

Part-c

When the length is doubled, in this case the new time period is

therefore

or

Thus the percentage change is

by plugging all the values we get