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.