The motion of a weight attached to a spring is governed by Hooke's Law: tension = k X

Chapter 5, Problem 6

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The motion of a weight attached to a spring is governed by Hooke's Law: tension = k X extension, where k is a constant of the spring. Consider the oscillations of the spring described in Figure 5 .11. x 1 and x2 are the displacements of weights of masses m1 and m2 at any instant. The extensions of the two springs at that instant are x1 and x2 - x1 Application of Hooke's Law gives the following equations of motion m1.X1 = -k1 x1 + k2(x2 - x1) and m2.X2 = -k2(x2 - x1) Figure 5.11 The general motion can be analyzed in terms of normal modes as in the example of this section. Analyze the motion when m1 = m2 = M, k1 = 3, and k2 = 2.