Normal Modes & Frequencies for Suspended Spring System: Masses 3m & 2m

[Benzoate]

Homework Statement

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.

Homework Equations

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.

 

[Benzoate]

anyone having trouble reading my problem?

 

[JasonJo]

Yeah I think you should rewrite it in LaTeX, I had a hard time trying to read it. I guess x(double dot) means second derivative of x? You should definitely retype it though, makes it easier for anyone who can help you.

 

[Benzoate]

Yeah I think you should rewrite it in LaTeX, I had a hard time trying to read it. I guess x(double dot) means second derivative of x? You should definitely retype it though, makes it easier for anyone who can help you.

I edited my OP. Are you able to read it any better?