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A bar of mass m is suspended horizontall...

A bar of mass `m` is suspended horizontally on two vertical springs of spring constant `k` and `3k`. The bar bounces up and down while remaining horizontal. Find the time period of oscillation of the bar neglect mass of springs and friction everywhere

A

`2pisqrt((m)/(k))`

B

`2pisqrt((m)/(3k))`

C

`pisqrt((2m)/(3k))`

D

`pisqrt((3m)/(4k))`

Text Solution

Verified by Experts

`x=` distance moved by rod
`x_(1)=` extension in the spring of spring constant `3k`.
`x_(2)=`extension in the spring of spring constant `k`.
`x_(1)+x_(2)=2x` (constant relation)
`3kx_(1)=kx_(2)`(tension in string is same)
`-(3kx_(1)+kx_(2))=m(d^(2)x)/(dt^(2))`
solving above `3` equations
`rArr T=2pisqrt((m)/(3k))`
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