In the arrangement shown, the sleeve of mass `M` is fixed between two identical springs whose combined force constant is `k`. The sleeve can slide without friction over a horizontal bar `AB`. The arragement rotates with a constant angular velocity `omega` about a vertical axis passing through the middle of the bar. the period of small oscillations of teh sleeve is.........

Options

A. `2pi sqrt((m)/(k))`
B. `2pi sqrt((m)/(k-m omega^(2)))`
C. `pi sqrt((m)/(k))`
D. `pi sqrt((m)/(k-m omega^(2)))`

Answer

B

Explanation

Let `x` be the displacement of sleeve in disturbed condition along horizontal bar from centre. The free body diagram is:

`:. F_("restoring") = kx - m omega^(2)x rArr ma =(k -m omega^(2))x`
`rArr a = ((k-momega^(2)))/(m)x T = ?`
[`:'` do not confuse angular velocity of frame with angular frequency of `SHM`]