First slide

Applications of SHM

Question

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

Moderate

A

1s
B

2s
C

3s
D

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

Solution

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

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