Problems for
Intermediate Methods in Theoretical Physics

Edward F. Redish

Two Carts with a Light Middle Spring

Two identical wheeled carts of mass m are connected between two walls as shown in the figure below.   The inner spring has spring constant k and the two outer springs have spring constants K = 10k. All three springs have a rest length l0 and the distance between the walls is L.

(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) Describe what the normal modes will be like.

(c) Find the normal modes and normal frequencies (expressed as a function of ) using any approach you want.


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Edward F. Redish
Department of Physics
University of Maryland
College Park, MD 20742
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Last revision 7. December, 2005.