First slide

Applications of SHM

Question

A mass m attached to a spring oscillates every 2 sec. If the mass is increased by 2 kg, then time-period increases by 1 sec. The initial mass is

Moderate

A

1.6 kg
B

3.9 kg
C

9.6 kg
D

12.6 kg

Solution

$T = 2 π \sqrt{\frac{m}{k}} \Rightarrow \frac{T_{2}}{T_{1}} = \sqrt{\frac{m_{2}}{m_{1}}} \Rightarrow \frac{3}{2} = \sqrt{\frac{m + 2}{m}} \Rightarrow \frac{9}{4} = \frac{m + 2}{m}$
$\Rightarrow m = \frac{8}{5} kg = 1 .6 kg$

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