Question

A simple pendulum of length L and mass M has frequency f. To increase its frequency to 2f

Answer 1

Given:

A simple pendulum of length L and mass M has frequency f.

To find:

What should be changed for the frequency to be 2f ?

Calculation:

General expression for frequency of a pendulum is :

$f = \dfrac{1}{2\pi} \sqrt{ \dfrac{g}{L} }$

Now, new frequency is 2f and let required length be L_(2).

$\therefore \: 2f = \dfrac{1}{2\pi} \sqrt{ \dfrac{g}{L_{2}} }$

$\implies\: 2 \bigg(\dfrac{1}{2\pi} \sqrt{ \dfrac{g}{L} } \bigg)= \dfrac{1}{2\pi} \sqrt{ \dfrac{g}{L_{2}} }$

$\implies\: 2 \sqrt{ \dfrac{1}{L} } = \sqrt{ \dfrac{1}{L_{2}} }$

$\implies\: \dfrac{4}{L} = \dfrac{1}{L_{2}}$

$\implies\:L_{2} = \dfrac{L}{4}$

So, the new length required is L/4 to make the frequency 2f.