Question

A simple pendulum is found to vibrate 50 times within 200seconds. When 1.5m of its length is reduced to a certain length, it vibrates 50 times in 175s. Find the original length of the pendulum.

Answer 1

Solution

First case is

50 times within 200 s corresponds to a period of

$T=\frac{200}{50}=4sec.$

The original length of the pendulum can be found from the period:

$T=2\pi \sqrt{\frac{l}{g}}$

So origional length

$l=\frac{gT^2}{4\pi^2}$

Putting all values

$l=\frac{9.8\times 4^2}{4\times(3.14)^2}$

$l=3.97m$