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Question 24

A mass $$m$$, attached to free end of a spring executes SHM with a period of 1 s. If the mass is increased by 3 kg, the period of oscillation increases by one second. The value of mass $$m$$ is _____ kg.

Correct Answer: 1

Solution

$$T = 2\pi\sqrt{\frac{m}{k}}$$

$$T \propto \sqrt{m}$$

$$\frac{T_2}{T_1} = \sqrt{\frac{m + 3}{m}}$$

$$\frac{2}{1} = \sqrt{\frac{m + 3}{m}}$$

$$4 = \frac{m + 3}{m}$$

$$m = 1\text{ kg}$$

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