A block of mass `m` connected with a smooth prismatic wedge of mass m is released from rest when the spring is relaxed. Find the angular frequency of oscillation.

Answer

`sqrt (((M + m) k)/(m (M + m sin^(2) theta)))`

Explanation

Force equiation for `(M + m)` in horizontal direction
`MA + m (a cos theta + A) = 0` (i)
For m w.r.t. M along the slop:
`Mg sin theta - mA cos theta - kx = ma` (ii)
Equation (i) and (ii) give `(d^(2) x)/(dt^(2)) + omega^(2) x = constant`
Hence, `omega = sqrt (((M + m) k)/(m (M + m sin^(2) theta)))`