1. The problem statement, all variables and given/known data A particle P of mass 3m is suspended from a fixed point O by a massless linear spring with strength alpha. A second particle Q of mass 2m is in turn suspended from P by a second spring of the same strength. The system moves in the vertical straight lie through O . Find the normal frequencies and the form of the normal modes for this system. Write down the form of the general motion. 2. Relevant equations 3. The attempt at a solution 3mx''= -alpha*x+alpha*(y-x) 2my''= -alpha*(y-x) dividing out m, my set of equations looks like: 3x''+2xn^2-yn^2=0 2y''+yn^2+xn^2=0 n^2=alpha/m Let x=A cos(omega*t-gamma) and y= B cos(omega*t-gamma) x''=-A*omega^2*cos(omega*t-gamma) y''=-B*omega^2*cos(omega*t-gamma) plugging x'' and y'' into two equations I get: 3(-A*omega^2)+2(A)n^2-(B)n^2=0 2(-B*omega^2])+Bn^2+ An^2=0 -omega^2*n^2+n^4=0 There is something wrong with how I set up my equations and I cannot spot my errors.