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A solid cylinder of mass m is attached t...

A solid cylinder of mass `m` is attached to a horizontal spring with force constant `k`. The cylinder can roll without slipping along the horizontal plane. (See the accompanying figure.) Show that the center of mass of the cylinder executes simple harmonic motion with a period `T = 2pisqrt((3m)/(2k))`, if displaced from mean position.

A

`(KA)/(3)sinomegat`

B

`Asinomegat`

C

`(3)/(2)Kacosomegat`

D

`Acosomegat`

Text Solution

Verified by Experts

The correct Answer is:
A
`kx_(1)-f=mw^(2)x_(1)`
`f=kx_(1)-mw^(2)x_(1)`
=`(k-(m)((2k)/(3m)))x_(1)=(k)/(3)x_(1)=(k)/(3)Asinomegat`
`f=(kA)/(3)sinwt`
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