First slide

Applications of SHM

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

9/16
B

25/16
C

4/5
D

5/4

Solution

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

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