Question

A swinging pendulum has a period of 17.0s when the length is shortened by 1.5m, it's period is 8.55 calculate the original length of the pendulum

Answer 1

The period of a simple pendulum is given by

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

So

$$T_0=2\pi\sqrt{l_0/g}=17.0\\ T=2\pi\sqrt{(l_0-1.5)/g}=8.55$$ $$\frac{l_0}{l_0-1.5}=3.95$$

$$l_0=3.95l_0-5.93$$

$$l_0=2.0\:\rm m$$