Ok basically we have two identical coupled pendula - each of length l with bobs of mass m connected by spring with spring constant k.
so I've shown the eqns of motion are mx'' = -mgx/l + k(y-x) and my'' = -mgy/l - k(y-x)
The question says: By looking for solutions where x and y vary harmonically at the same angular freqency w, convert these differential equations into two ordinary simultaneous equations for the amplitudes of oscillation X and Y.
Then it says why do you not expect these eqns to determine the absolute values of X and Y
The Attempt at a Solution
So I think I know the answer to the second q - we lack initial conditions, which are necessary to find absolute values of X and Y..
Im just not sure how to convert the two DEs into ordinary simulateous eqns for X and Y