Find the normal modes of oscillation for small-amplitude motions of a double pendulum (a lower mass \(m\) hanging from an upper mass \(M\) ) where the pendulum lengths are equal. Find the normal mode frequencies and the amplitude ratios of \(M\) and \(m\) in each case. Let the generalized coordinates be \(\theta_{1}\), the angle of the upper mass relative to the vertical, and \(\theta_{2}\), the angle of the lower mass relative to the vertical.