Instructions: Solve the problem in the left column and note the steps you took to solve it in the right column. This problem was taken from a graduate level physics course. The purpose of this exercise is to think about the steps you went through to solve the problem, not to arrive at the solution. Therefore, do not focus on algebra, but instead on getting the problem to a point that algebra is all that is left. With this in mind, I could have put a problem here that was extremely complicated (think Jackson E&M), but due to time constraints, decided on an easier (but still advanced, so don't worry if you do not know how to do it) problem. Use the back of this page as necessary.
A point particle of mass m is connected to a massless rod of length s. The rod is hinged (frictionless hinge). The hinge is constrained to oscillate vertically with harmonic motion
hhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhh h(t) = a + h0 cos ωt
where a and h0 are constants and h0 < a. The system is moving in a homogeneous gravitational field. What are the equation(s) of motion for the particle?