First slide

Simple hormonic motion

Question

A spring has a force constant k and a mass m is suspended from it. The spring is cut in half and the same mass is suspended from one of the halves. If the frequency of oscillation in the first case is $α$ , then the frequency in the second case will be

Moderate

A

2 $α$
B

$α$
C

$α / 2$
D

$α \sqrt{2}$

Solution

$T = 2 π \sqrt{(\frac{m}{k})} or α = \frac{1}{2 π} \sqrt{(\frac{k}{m})} When the spring is cut into trvo equal parts, each part has a spring coustant 2 K . Hence α_{1} = \frac{1}{2 π} \sqrt{(\frac{2 k}{m})} = \sqrt{2} [\frac{1}{2 π} \sqrt{(\frac{k}{m})}] = \sqrt{2} \cdot α$

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