First slide

Applications of SHM

Question

A mass M is suspended from a light spring. An additional mass m added displaces the spring further by a distance x. Now the combined mass will oscillate on the spring with period

Moderate

A

$T = 2 π \sqrt{(mg / x (M + m))}$
B

$T = 2 π \sqrt{((M + m) x / mg)}$
C

$T = (π / 2) \sqrt{(mg / x (M + m))}$
D

$T = 2 π \sqrt{((M + m) / mgx)}$

Solution

As mg produces extension x, hence $k = \frac{mg}{x}$
$∴ T = 2 π \sqrt{\frac{(M + m)}{k}} = 2 π \sqrt{\frac{(M + m) x}{mg}}$

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