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

Options

A. `2pisqrt((m)/(k))`
B. `2pisqrt((m)/(3k))`
C. `pisqrt((2m)/(3k))`
D. `pisqrt((3m)/(4k))`

Explanation

`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))`