(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.
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Last revision 28. October, 2004.