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For the system given below, find the ang...

For the system given below, find the angular frequency of oscillation?

A

`(10)/(sqrt(3))`

B

`10sqrt(3)`

C

`(20)/(sqrt(3))`

D

`20sqrt(3)`

Text Solution

Verified by Experts

The correct Answer is:
C
By energy method
`(1)/(2)Kx^(2)+(1)/(2)mv^(2)+(1)/(2)Iomega^(2)=C`
`(1)?(2).K.2x.(dx)/(dt)+(1)/(2).m.2v.(dv)/(dt)+(1)/(2)I.(2v)/(r^(2))(dv)/(dt)=0`
`Kxv+(M)/(4)va+(M)/(2)a.v=0`
`-Kx=(3Ma)/(4)`
`a=-(4K)/(3M)=.x=-omega^(2)x`
`omega^(2)=(4K)/(3M)`
`omega=sqrt((4K)/(3M))=sqrt((4xx100)/(3xx1))=(20)/(sqrt(3))`rad/sec
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