First slide

Simple hormonic motion

Question

A mass M is suspended from a spring of negligible mass. The spring is pulled a little and then released so that the mass executes simple harmonic oscillations with a time period T. If the mass is increased by m then the time period becomes( $\frac{5}{4} T$ ). The ratio of $\frac{m}{M}$ is

Moderate

A

$\frac{9}{16}$
B

$\frac{25}{16}$
C

$\frac{4}{5}$
D

$\frac{5}{4}$

Solution

$T = 2 π \sqrt{\frac{m}{K}} \Rightarrow m \propto T^{2} \Rightarrow \frac{m_{2}}{m_{1}} = \frac{{T^{2}}_{2}}{{T^{2}}_{1}}$
$\Rightarrow \frac{M + m}{M} = {(\frac{\frac{5}{4} T}{T})}^{2} \Rightarrow \frac{m}{M} = \frac{9}{16}$

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