Derive the equation of motion of the mass \(m\) shown in Fig. 3.67 when the pressure in the cylinder fluctuates sinusoidally. The two springs with stiffness \(k_{1}\) are initially under a tension of \(T_{0}\), and the coefficient of friction between the mass and the contacting surfaces is \(\mu\).

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p(t) = Po sin ot 000= k www m To k x(1) k To -x(t) FIGURE 3.67 Motion of mass subjected to sinusoidal pressure.