I've found the characteristic equation of the system I'm trying to solve:
$$ω^{4}m_{1}m_{2}-k(m_{1}+2m_{2})ω^{2}+k^{2}=0$$
I now need to find the eigenfrequencies, i.e. the two positive roots of this equation, and then find the corresponding eigenvectors. I've been OK with other examples, but because of the different masses here, I don't see any obvious substitution or cancellation that will leave the eigenfrequencies in a manageable form.
I've been at this a while and I'm a bit lost.
Thanks in advance.
$$ω^{4}m_{1}m_{2}-k(m_{1}+2m_{2})ω^{2}+k^{2}=0$$
I now need to find the eigenfrequencies, i.e. the two positive roots of this equation, and then find the corresponding eigenvectors. I've been OK with other examples, but because of the different masses here, I don't see any obvious substitution or cancellation that will leave the eigenfrequencies in a manageable form.
I've been at this a while and I'm a bit lost.
Thanks in advance.
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