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Today I took the first session of the comprehensive exams, in the physics deprtment of gatech. The subject was classical mechanics.
The problems were fairly known, first one, a bead in a rod, capable of sliding, while the rod moves with constant angular velocity. Were asked to prove that a possible solution to the equation of the motion has exponential shape, and find the generalized forces.
Second one, a marble in a dish (circular shape), find the small oscillations frequency.
Third one, a block on a wedge. The wedge moves with "horizontal" acceleration. Were asked to find what was the value of the acceleration that kept the block for sliding, if tangent of the angle was higher than the frictio ncoefficient between the block and the wedge.
Fourth, the equation of the rocket in the gravitational field.
Fifth, given the hamiltonian, find the lagrangian.

Easy cake! Hope tomorrow is this easy also!.