First slide

Simple hormonic motion

Question

A block of mass M is suspended by a spring and allowed to oscillate vertically with time period 1 second wen another block of mass m is attached to the block of mass M and allowed to oscillate vertically, the time period is found to be 2 sec then, M/m is equal to

Moderate

A

3
B

1/2
C

1/3
D

2

Solution

$2 π \sqrt{\frac{M}{K}} = T_{1} and 2 π \sqrt{\frac{M + m}{K}} = T_{2}$
$∴ \sqrt{\frac{M + m}{M}} = \frac{T_{2}}{T_{1}} \Rightarrow \frac{m}{M} = {(\frac{T_{2}}{T_{1}})}^{2} - 1 = {(2)}^{2} - 1 = 3 \Rightarrow \frac{M}{m} = \frac{1}{3}$

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