University of Alabama in Huntsville
Department of Physics
Fall 2008
PH 601: Classical Dynamics I
Homework Problem Set No. 5
Deadline: 13 October, 2008
Problem 21:
Two identical and massless rods of length `are connected to a horizontal
bar at a distance afrom each other. The gravitational acceleration is g.
Two identical masses mare connected to the lower ends of the rods, and are
connected to each other by a spring of equilibrium length aand spring con-
stant k. Show that the matrix formed from the eigenvectors simultaneously
diagonalizes both the kinetic energy matrix and the potential energy matrix.
Problem 22:
A mass Mis constrained to move along a horizontal and frictionless wire. A
second mass mis connected to Mthrough a massless rod of length b. The
gravitational acceleration is g. The system can move and oscillate only in
the plane of the wire and the direction of the gravitational acceleration. Find
the normal modes and the normal coordinates.
Problem 23:
Two identical masses mare connected by identical and massless rods of length
b, so that the second rod is connected to the mass at the end of the first rod
and the second mass is connected at the end of the second rod. (Same setup
at that of problem 12.) Find the normal frequencies and the normal modes.
Assume two dimensional motion.
Problem 24:
Three identical masses mare connected by four identical springs of spring
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