Problems for
Intermediate Methods in Theoretical Physics

Edward F. Redish

Three Coupled Oscillators

Three identical carts are connected to exterior walls by four identical springs as shown in the figure.

(a) Using coordinates, yi that are horizontal, have their positive direction to the right, and have their 0 at the i-th cart's equilibrium position, (i = 1, 2, 3) write the laws of motion for the three carts starting with Newton's second law. Ignore friction and air resistance.

(b) Find the normal modes and natural frequencies for this system. Express your frequencies as a multiple of the natural frequency parameter, ω0 = (k/m)1/2.

(c) Explain the motion of the carts in each normal mode and, if you can, explain physically why the frequencies associated with each mode are what they are what they are.

RETURNS

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This page prepared by

Edward F. Redish
Department of Physics
University of Maryland
College Park, MD 20742
Phone: (301) 405-6120
Email: redish@umd.edu

Last revision 28. October, 2004.