Question

A simple pendulum is found to vibrate 50 times within 200s. 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

50 times within 200 s corresponds to a period of

$$T=\frac{200}{50}=4\text{ s}.$$

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

$$T=2\pi\sqrt{\frac{l}{g}},\\\space\\ l=\frac{gT^2}{4\pi^2}=3.97\text{ m}.$$