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Question

# Find the time period of the spring mass system shown in the figure below.

A
T=2πm2K
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B
T=2πmK
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C
T=2π2mK
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D
T=2π3m2K
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Solution

## The correct option is B T=2π√mKFrom the diagram we can deduce that, forces balance only when there is elongation x0 in the spring. At point of equilibrium, Fnet=0 ⇒mgsinθ=Kx0 ……(1) where x0 is elongation in the spring at natural length. Let us displace the spring further by x. Then, Fnet=mgsinθ−Kx−Kx0 Using (1) in the above equation, we get Fnet=−Kx ⇒a=−(Km)x Comapring this with a=−ω2x, we get ω=√Km ⇒T=2πω=2π√mK Thus, option (b) is the correct answer.

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