advertisement

PHYS 4423 FALL 2014 Assignment #6; Due Thursday, October 30 Read Sections 12.1 to 12.8 in Chapter 12 1. A mass of m is suspended from a support by a string with spring constant m𝜔12 . A second mass m is suspended from the first mass by a spring constant m𝜔22 . A vertical harmonic force Fo 𝑐𝑜𝑠𝜔𝑡 is applied to the upper mass. Find the steadstate motion for each mass. Examine what happens when 𝜔 = 𝜔2 . 2. A model of a ring molecule consists of three equal masses m which slide without friction on a fixed circular wire of radius R (see figure). The masses are connected by identical springs of spring constant mω2 . The angular positions of the three masses, θ1, θ2, θ3 are measured from a rest position. (a) Write down the Lagrangian and show that the equations of motion are θ1 ω2 2θ1 θ2 θ3 0 θ2 ω2 2θ2 θ1 θ3 0 θ3 ω2 2θ3 θ1 θ2 0 (b) Show that the mode in which θ1 θ2 θ3 corresponds to 3 constant angular momentum L pθi i 1 3. Do problem 12-3 on pages 507.