Find time period of oscillation of the system.

Explanation

`m_(1) (d^(2)x_(1))/(dt^(2)) = -Kx`
`m_(2) (d^(2)x_(2))/(dt^(2)) =- Kx`
Now, `x_(1) + x_(2) = x`
or `(d^(2)x_(1))/(dt^(2)) + (d^(2)x_(2))/(dt^(2)) = (d^(2)x)/dt^(2) rArr" "(-Kx)/(m_1) - (Kx)/(m_(2)) =- omega^(2)x`
`omega = sqrt((K)/(m_(1)) + (K)/(m_(2)))" "&" "T = (2pi)/(omega)`