Question

Pendulum A has a bob of mass m hung from the string of length L; pendulum B is identical to A except its bob has the length 2L. Compare the frequencies of small oscillations of the two pendulums.

Answer 1

Answer:

$f_{B}: f_{A} = \sqrt{\frac{2}{1}}$

Explanation:

For pendulum A: Length = L and gravity = g

The frequency of pendulum A is given by

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

Here, f is the frequency, L be the length

$f_{A} = \frac{1}{2\pi }\sqrt{\frac{g}{L}}$     ... (1)

For pendulum B: Length = 2L, gravity = g

The frequency of pendulum B is given by

$f_{B} = \frac{1}{2\pi }\sqrt{\frac{g}{2L}}$   .... (2)

Divide equation (1) by (2)

$f_{B}: f_{A} = \sqrt{\frac{2}{1}}$