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Complex eigenvectors help I'm currently working on a physics problem involving six identical masses arranged in a circle, attached to each other via identical springs. My job is to find the normal modes using a symmetry matrix and its corresponding eigenvectors and eigenvalues. Since I'm working with 6 masses, I get a 6x6 symmetry matrix to fulfill the eigenvector/eigenvalue equation SA=BA, where S^6=I, which means there are six normal modes (some are complex) that I can work with. The problem is that when I tried solving for the general form of the eigenvector B, I found that the components of B (I'll denote them b) follow this fancy equation: b^6=1. I already know that this has 2 real values and 4 complex ones, but first I need to provide

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Physics problem help So, this last problem on my final completely destroyed me, and it's been bugging me ever since I got back home. Can someone solve this and show me the work so my soul can be at peace? My physics professor called it a Gyroscope of Doom, by the way. Suppose there is an L-shaped rod (think half of a square's perimeter), with a side length L and total mass M. The rod is attached to the z-axis at the origin but is tilted an angle T below the xy plane, so it makes some sort of a tilted letter 'V' when viewed horizontally. At the end of the rod is a disc of radius R and mass M, which is spinning at an angular velocity w. Gravity is acting on the system's center of mass (not given). In addition, a spring of rest length 0 and sp

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Some Physics Help Okay so I have this physics problem on the momentum space representation of wavefunctions. I already made all the necessary physical arguments; given a wavefunction in momentum space, which must be normalized, the Fourier Transform into the position space must not affect its normalization in position space. So I defined a somewhat arbitrary wavefunction in momentum space (it's a pretty generic form) and had to solve for N as shown in the link below: [url=http://i286.photobucket.com/albums/ll92/cb000/MomentumSpaceproblem.png]Here it is.[/url] I'm very confident in my physical arguments, but when it comes to solving for N, I can't seem to make it normalize in the position space. When I run the momentum space wavefunction thr

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Physics Help I'll first give the problem [url=http://i286.photobucket.com/albums/ll92/cb000/physicshelp_zpsb649b48b.png]here[/url]. The text in green is the problem, and the stuff written in orange includes my work. I know the partition function, the Debye Temperature, and how to get the mean pressure from the partition function. I've made the integral approximation for the sum, and I've juggled some substitutions to get the integral in a form without too many extraneous constants. But when it comes down to doing the actual derivative, it seems that I have to do some calculus magic to get it in some coherent form. I'm not really a mathematician, so I'm stuck here. Anyone care to help?