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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=2πmK
From 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=mgsinθKxKx0


Using (1) in the above equation, we get
Fnet=Kx
a=(Km)x
Comapring this with a=ω2x, we get
ω=Km
T=2πω=2πmK
Thus, option (b) is the correct answer.

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