First slide

Applications of SHM

Question

Three masses 700g, 500g, and 400g are suspended at the end of a spring a shown and are in equilibrium. When the 700g mass is removed, the system oscillates with a period of 3 seconds, when the 500 gm mass is also removed, it will oscillate with a period of

Moderate

A

1 s
B

2 s
C

3 s
D

$\sqrt{\frac{12}{5}} s$

Solution

When mass 700 gm is removed, the left out mass (500 + 400) gm oscillates with a period of 3 sec
$∴ 3 = t = 2 π \sqrt{\frac{(500 + 400)}{k}}$ …...(i)
When 500 gm mass is also removed, the left out mass is 400 gm.
$∴ t^{'} = 2 π \sqrt{\frac{400}{k}}$ …..(ii)
$\Rightarrow \frac{3}{t^{'}} = \sqrt{\frac{900}{400}} \Rightarrow t^{'} = 2 \sec$

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