Two small masses $m$ are connected and hung between walls by weightless strings as pictured below. The acceleration due to gravity is $g$. All oscillatory motion is assumed to have a small amplitude and the system is always in one of its normal modes (i.e. the oscillations are sinusoidal).

i  ^2.00 Find $\omega_{1}$, the angular frequency of in-phase oscillations (by which the oscillation phases of the both masses are always equal), perpendicular to the plane of the figure.

ii  ^3.00 Find $\omega_{2}$, the angular frequency of anti-phase oscillations (by which the oscillation phases of the both masses are always opposite), in terms of $\omega_{1}$.