Problem 5-12 Using the approximation of small oscillations, and starting from F

Question

Problem 5-12

Using the approximation of small oscillations, and starting from F = ma, derive the equations of motion of M1 and M2: For M1 = M2 = M, use the equation to obtain the normal frequency of the system. What are the normal-mode motion for M1 = M2 = M and ? Two equal masses m are connected to three identical springs (spring constant k) on a frictionless horizontal surface (see figure). One end of the system is fixed; the other is driven back and forth with a displacement X = X0 cos omega t. Find and sketch graphs of the resulting displacements of the two masses. A string of length 3l and negligible mass is attached to two fixed support at its ends. The tension in the string is T.

Explanation / Answer

since all the springs and masses are equal , displacement of A = 2X/3coswt and B = x/3coswt

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