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Find out natural frequency of given system.
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Dist of CG from surface = (4r3π)

ANSLOM

IT = of all moments

+Ioθ=mgsinθ×(4r3π)

sinθθ

Ioθ=mgθ(4r3π)

Ioθ+mg(4r3π)θ=0

θ+mg(4r3π)θ=0

θ+mg(4r3π)θIo = 0

wn=mg(4r3π)Io

where =Io=mR22

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