Find the period of the oscillations of the devices shown in figure if `m` is displaced slightly.

Explanation

Reduced mass of the system
(1) `mu = ((mM)/(m+M))`
`:. T_(1) = 2pi sqrt((mu)/(K)) = 2pi sqrt((mM)/((m+M)K))`
(2) `mu = (mm)/(m+m) = (m)/(2)` and `K_(e) = K+K = 2K`
`:. T_(2) = 2pi sqrt((mu)/(K_(e))) = 2pi sqrt(m)/(4K)`