1. The problem statement, all variables and given/known data Two identical pendulums of the same mass m are connected by a light spring. The displacements of the two masses are given, respectively, by xa = Acos( (w2-w1)t/2 )cos( (w2 + w1)t/2 ), xb = Asin( (w2-w1)t/2 )sin( (w2 + w1)t/2 ). Assume that the sprint is sufficiently weak that its potential energy can be neglected and that the energy of each pendulum can be considered to be constant over a cycle of its oscillation. Show that the energies of the two masses are are: Ea = 1/2 m * A^2 ( (w2 + w1)/2 )^2 cos^2( (w2 - w1)t/2 ) Eb = 1/2 m * A^2 ( (w2 + w1)/2 )^2 sin^2( (w2 - w1)t/2 ) 2. Relevant equations Energy of simple harmonic oscillator = (1/2)mw^2 (amplitude)^2 3. The attempt at a solution In the book's solution, it says that amplitude = A cos[ (w2 - w1)t/ 2] or A sin[ (w2 - w1)t/2 ]. Where does it get this from? What happened to the other cosine/sine term? Why is it using this particular term?