First slide

Simple hormonic motion

Question

The system shown in Fig. is initially in equilibrium. When the 500 gm mass is removed, the system oscillates with a time period 4 sec. On removing the 700 gm mass also, time period of oscillation will be:

Moderate

A

2 sec
B

3 sec
C

4 sec
D

5 sec

Solution

When 500 gm mass is removed then
$π = 2 π \sqrt{\frac{(900 + 700)}{k}} = 4 \sec$
When 700 gm mass is removed then
$T' = 2 π \sqrt{\frac{900}{k}} \Rightarrow \frac{T'}{T} = \sqrt{\frac{900}{1600}} = \frac{3}{4} \Rightarrow T' = 3 \sec$

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