Answer to Question #239386 in Physics for PXT

Question

To increase the oscillation period of a simple pendulum by 41%, how much change is required in its effective length?

Answer 1

Given:

$T=1.41T_0$

The period of oscillation of a simple pendulum is given by

$$T_0=2\pi\sqrt{\frac{l_0}{g}}$$

So

$$1.41T_0=2\pi\sqrt{\frac{l}{g}}$$

$$1.41*2\pi\sqrt{\frac{l_0}{g}}=2\pi\sqrt{\frac{l}{g}}$$

$$1.41\sqrt{l_0}=\sqrt{l}$$

Finally,

$$l=1.99l_0$$

Answer: the length should to be increased by $99\%.$