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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.

Respuesta :

Answer:

[tex]f_{B}: f_{A} = \sqrt{\frac{2}{1}}[/tex]

Explanation:

For pendulum A: Length = L and gravity = g

The frequency of pendulum A is given by

[tex]f = \frac{1}{2\pi }\sqrt{\frac{g}{L}}[/tex]

Here, f is the frequency, L be the length

[tex]f_{A} = \frac{1}{2\pi }\sqrt{\frac{g}{L}}[/tex]     ... (1)

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

The frequency of pendulum B is given by

[tex]f_{B} = \frac{1}{2\pi }\sqrt{\frac{g}{2L}}[/tex]   .... (2)

Divide equation (1) by (2)

[tex]f_{B}: f_{A} = \sqrt{\frac{2}{1}}[/tex]

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