Derive the equation of motion and natural frequency for mass \(m\) shown in Figure 2.53. Assume the pulleys are massless, the cable is inextensible, and let the spring constant be \(k\). The coordinate \(y\) is the displacement of its center of mass, measured from the static equilibrium position, and the coordinate \(x\) is the displacement of the center of mass measured from its location when the spring is unstretched.

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position of m when the spring is unstretched static equilibrium y position m eeeee k Figure 2.53: A mass suspended in a pulley system.