Q.

For the arrangement shown in the figure, find the period of oscillation

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a

2π2mk

b

2πm4k

c

2π4mk

d

2πmk

answer is C.

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Detailed Solution

When the block displaced down by x, the spring will stretch by x2  From the free body diagram of the pulley, kx2 =2T  or T=kx4The net restoring force on the block is T. Using the Second Law of motion, we get md2xdt2=-T=-kx4d2xdt2=-kx4m=ω2x ω=k4m      T=2π4mk
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