Derive the equation of motion and natural frequency for mass \(m\) shown in Figure 2.58. Assume the pulleys are massless, and let the spring constants be \(k_{1}\) and \(k_{2}\). Let \(x_{1}\) and \(x_{2}\) be the displacements of the pulley and the mass measured from their locations when the springs are unstretched. Use \(x_{2}\) for the equation of motion.

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x1 k k ellee eeeee m X2 Figure 2.58: A mass suspended by a pulley and springs.