It seems like we arrive at the same eigenvectors which is reassuring. Thanks for all your hard work on this problem.
I am becoming skeptical that normal modes exist for cases when the masses are different or the sping constant connecting m1 to the wall is different than the spring constant...
It was a typo. If you sub the "normal coordinates" just found into the equations of motion you will find they do not separate as they should. Or I don't see how they separate.
Yes, this sounds similar to what I did. I made an error in my original post regarding the eigenvectors :blushing:. The correct eigenvectors are:
a_{j (1)} = \left(1, \frac{1}{m_2} \left( - m_1 + m_2 + \sqrt{m_1^2 - m_1 m_2 + m_2^2} \right) \right)
a_{j (2)} = \left(1, \frac{1}{m_2} \left( -...
The eigenvalue equation is
\left( 2 k - \omega^2 m_1 \right) \left( 2 k - \omega^2 m_2 \right) - k^2 = 0
which has two roots in the variable \omega^2:
\omega^2_{\pm} = \frac{k}{m_1 m_2} \left( m_1 + m_2 \pm \sqrt{m_1^2 - m_1 m_2 + m_2^2} \right)
You are right, there is a rediculous...
Homework Statement
A particle of mass m1 is attached to a wall by a spring of constant k. A second particle of mass m2 is attached to a different wall by another sping of constant k. The two masses are attached to each other by a third spring of constant k. Let x_1 and x_2 be the displacement...
Thanks for your response. I would not say G.R. trumps special relativity, rather, special relativity exists as a limiting case of G.R. I put my query in terms of special relativity because it is easier to understand and my example does not require the full analysis of G.R. (as far as I can...
I think this is an excellent question. I have spent some time thinking about it, but without much success. The original answer given by pervect is good, but I have one question and a comment.
Has anyone gone to the frame of reference where the CMB is isotropic and measured it from there? Or is...