Question

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

Answer 1

For original length:

$$\frac{T_1}{N_1}=2\pi\sqrt{\frac{l}{g}},\\\space\\ l=g\bigg(\frac{T_1}{2\pi N_1}\bigg)^2=3.97\text{ s}.$$