A mass attached to the 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 is ______ kg. [2023]

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Solution

Q.
A mass $m$ attached to the 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. [2023]

Ans.
(1)

$T = 2 π \sqrt{\frac{m}{k}} = 1$

$T' = 2 π \sqrt{\frac{m + 3}{k}} = 2$

$\frac{T}{T'} = \sqrt{\frac{m}{m + 3}} = \frac{1}{2}$

$\Rightarrow \frac{m}{m + 3} = \frac{1}{4} \Rightarrow m = 1$

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