First slide

Simple hormonic motion

Question

What will be time period of the displaced body of mass m?

Moderate

A

$2 π \sqrt{\frac{m}{2 k}}$
B

$2 π \sqrt{\frac{3 m}{k}}$
C

$2 π \sqrt{\frac{3 m}{2 k}}$
D

$π \sqrt{\frac{3 m}{k}}$

Solution

Equivalent force constant of three springs,
$k_{eq} = \frac{k_{1} k_{2}}{k_{1} + k_{2}} = \frac{k \times 2 k}{3 k} = \frac{2 k}{3}$
$T = 2 π \sqrt{\frac{m}{k_{eq}}} = 2 π \sqrt{\frac{m}{2 k / 3}}$
$\Rightarrow T = 2 π \sqrt{\frac{3 m}{2 k}}$

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