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

For the original length, we have:

$$\frac{T_o}{N_o}=2\pi\sqrt{\frac{l}{g}},\\\space\\ l=g\bigg(\frac{T_o}{2\pi N_o}\bigg)^2=3.97\text{ s}.$$