Consider the spring-mass system depicted in Figure AP8.6. Develop a transfer function model to describe the motion of the mass M = 2 kg, when the input is u(t) and the output is x(t). Assume that the initial conditions are x(0) = 0 and x(0) = 0. Determine values of k and b such that the maximum steady-state response of the system to a sinusoidal input u(t)= sin(ωt) is less than 1 for all ω. For the values you selected for k and b, what is the frequency at which the peak response occurs?

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FIGURE AP8.6 Suspended spring-mass system with parameters k and b. x(t) ww u(t)