First slide

Simple hormonic motion

Question

Masses m and 3m are attached to the two ends of a spring of spring constant k.If the system vibrates freely, the period of oscillation will be:

Moderate

A

$π \sqrt{\frac{m}{k}}$
B

$2 π \sqrt{\frac{3 m}{k}}$
C

$π \sqrt{\frac{3 m}{k}}$
D

$2 π \sqrt{\frac{m}{k}}$

Solution

By reduced mass concept, $μ = \frac{m (3 m)}{m + 3 m} = \frac{3}{4} m$
$T = 2 π \sqrt{\frac{μ}{k}} = 2 π \sqrt{\frac{3 m}{4 k}} = π \sqrt{\frac{3 m}{k}}$

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