# Search results

1. ### A falling pendulum question

Homework Statement Hi, this is supposed to be an easy question, but for some reason I can't get it to work. The question is: A weightless rod is hinged at O so that it can rotate without friction in a vertical plane. A mass m is attached to the end of the rod A, which is balanced...
2. ### Statistical Physics - counting states

1. Homework Statement [/b] There are N 3-dimensional quantum harmonic oscillators, so the energy for each one is: E_i = \hbar \omega (\frac{1}{2} + n_x^i + n_y^i + n_z^i). What is the total number of states from energy E_0 to E, and what is the density of states for E? The Attempt at a...
3. ### Small Oscillations around equilibrium

Homework Statement The problem is: A point pendulum is being accelerated at a constant acceleration of a. Basically what's required is to find the equations of motion, the equilibrium point, and to show that the frequency of small oscillations about the e.p. is: \omega=L^{-1/2}...
4. ### Classical mechanics - Lagrange multipliers

Homework Statement A disk moves on an inclined plane, with the constraint that it's velocity is always at the same direction as it's plane (similar to an ice skate, maybe). In other words: If \hat{n} is a vector normal to the disk's plane, we have at all times: \hat{n} \cdot \vec{v} = 0. Also...
5. ### Frequency of oscillating cylinder

Homework Statement The problem is this: Find the angular frequency of the system in the figure when it's displaced at a small angle from equlibrium, given that ρ_0 < ρ_1. There is friction with the ground, so the motion is a rolling motion, without slipping. Homework Equations I used...