(adsbygoogle = window.adsbygoogle || []).push({}); 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.

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# Homework Help: Normal modes problem

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