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Applications of SHM

Question

A mass M attached to a spring oscillates with a period of 2 s. If the mass is increased by 2kg, the period increases by one second. The initial mass M (in kg) is ______.

Moderate
Solution

We know that for a spring block system T=2πMk

Here k = spring constant.

 In first case, 2=2πMk  ……….(i)

 In second case, 3=2πM+2k ………(ii)

Squaring of Eqs. (i) and (ii) and then dividing (ii) by (i), we have

94=M+2M=1+2M

Solving we get M = 1.6 kg.



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