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Q.

A uniform square plate of mass m is supported in a horizontal plane by a vertical pin at B and is attached at A to a spring of constant K. If corner A is given a small displacement and released, determine the period of the resulting motion

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a

2π2m3k

b

2πm6k

c

πm3k

d

m3k

answer is A.

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Detailed Solution

[Step 1]:  τ=Iα         [Step 2]:  Fb=23mb2α[Step 3]:  −kbx=2mb2α3[Step 4]:  α=3kx2mb​⇒ab=3kx2mb​⇒a=3kx2m​comparing with a=−ω2x​we get ω2=3k2m​[Step 5]:  ω=3k2m[Step 6]:  T=2π2m3k
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