First slide

Applications of SHM

Question

A weightless spring which has a force constant oscillates with frequency n when a mass m is suspended from it. The spring is cut into two equal halves and a mass 2m is suspended from it. The frequency of oscillation will now become

Moderate

A

$n$
B

$2 n$
C

$n / \sqrt{2}$
D

$n {(2)}^{1 / 2}$

Solution

$n = \frac{1}{2 π} \sqrt{\frac{k}{m}} \Rightarrow \frac{n}{n^{'}} = \sqrt{\frac{k}{m} \times \frac{m^{'}}{K^{'}}} = \sqrt{\frac{k}{m} \times \frac{2 m}{2 K}} = 1 \Rightarrow n^{'} = n$

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