Problems for
Intermediate Methods in Theoretical Physics

Edward F. Redish

Two Carts and Two Springs

Two identical wheeled carts of mass m are connected to a wall and each other as shown in the figure below. The two springs have spring constants k and a rest length l0.

(a) Choose a convenient coordinate system for describing the positions of the carts and write the equations of motion for the carts.   Be sure to specify your coordinate system.

(b) Do you have some way to check that these equations are right?   Describe one check you made.

(c) Find the frequencies of oscillation of the possible normal modes of the system.

(d) Our "standard normal modes"   and   that we have found for many systems are not normal modes of this system.   Explain why not.   (You don't have to find the actual modes.)


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

Last revision 13. November, 2005.