need help A box of mass m = 0.5 kg is suspended by a cable wrapped around the ou

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A box of mass m = 0.5 kg is suspended by a cable wrapped around the outer section of a cylindrical drum of radius R = 0.2 m as shown in Figure 2. A spring of stiffness k = 2500 N/m is attached to another cable that wraps about the smaller section of the drum, of radius r = 0.1 m, while the opposite end of the spring is attached to ground. Both cables are assumed not to stretch and the moment of inertia of the drum about its centre of mass is = 0.04 kg m2. The viscous-friction coefficient between the drum and a fixed surface is denoted by cT = 2 N m s. The system is initially (t = 0) in static equilibrium with theta = 0. The motion of the system is induced by an external moment M(t) applied to the drum. Write the dynamic model of the system in ODE form taking theta as the output variable. If the system is disturbed away from its equilibrium by initial conditions theta (0_) = phi/12 rad and theta (0_) = 0 rad/s: Will it oscillate as it returns to its equilibrium configuration? If so, at what frequency (in Hz)? How long will it take for the system to have returned to its static equilibrium? If an input M(t) = 5ua(t) N-m is applied to the drum at t = 0, compute the value of theta when t = 0.1 s t = 0.5 s

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