For the two-mass system shown in Figure 2.54 derive the equation of motion in terms of \(x_{1}\). Assume the pulleys are massless, the cable is inextensible, and let the spring constant be \(k\). The coordinates \(y_{1}\) and \(y_{2}\) are the displacements of the center of mass of \(m_{1}\) and \(m_{2}\), respectively, measured from the static equilibrium position. The coordinates \(x_{1}\) and \(x_{2}\) are the displacements of the center of mass of \(m_{1}\) and \(m_{2}\), respectively, measured from its location when the spring is unstretched.

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static equilibrium position for mul m G static equilibrium X2 Y2 position for m m2 Xeq2 eeeee Figure 2.54: Two masses suspended in a pulley system.