Equations (1) can be derived by drawing a free-body

Chapter 7, Problem 17

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Equations (1) can be derived by drawing a free-body diagram showing the forces actingon each mass. Figure 7.1.3a shows the situation when the displacements x1 and x2 of thetwo masses are both positive (to the right) and x2 > x1. Then springs 1 and 2 are elongatedand spring 3 is compressed, giving rise to forces as shown in Figure 7.1.3b. Use Newtonslaw (F = ma) to derive Eqs. (1).k1 k2x1 x2k3(a)m1 m2F1(t) k1x1 k2(x2 x1)k2(x2 x1) k3x2F2(t)m1 m2(b)FIGURE 7.1.3 (a) The displacements x1 and x2 are both positive.(b) The free-body diagram for the springmass system.

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