in attached mathcad 15 sheet, please scroll down to three red arrows(pg 4) where i tried to solve the equation in three different ways, but non worked. this problem can be thought of as an eigen value& eigen vector problem. i am trying to solve for the eigen vector corresponding to a certain frequency.
what is the mistake in my setup ? How can I fix it?
Maybe I misunderstand what you are trying to do, but the way I read it is that you set lambda="rhs expression", and substitute that into the matrix on the lhs, which yields the matrix on the rhs. The problem is, such a substitution will not result in the matrix on the rhs. Initially I thought all your diagonal terms were wrong, but in fact all terms other than the zeros are wrong. If that's what you are trying to do, anyway . If not, you need to explain in more detail the steps you are taking and why you think the solutions(s) are wrong.
The third method needs a value for m.1 and the assignment := instead of = for omega.1 as shown.
The first method has three equations and only two unknowns. The m.1's all cancel. Put the omega.1 variable back in and solve for it too.
It found 6 solutions.
Method 2 has the same problem as method 1...
I believe Mr. Jackson is mistaken. (This is dangerous ground!)
I believe some of your problem is unit balance. Symbolics doesn't understand units. To solve that you didn't give E, I, and h any units, you just typed the unit next to the number. The issue with that approach is that the problem does not scale properly, so your solutions for omega are not correct. The attached file fixes that.
But there's another issue: when solving for the Eigen Vectors, your mass cancels out. I can get Mathcad to give me eigenvalues and eigenvectors, but applying your method 2 results in a quandary.
Maybe the attached can move you forward, but I'm out of my depth here.