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Benzoate
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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.
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