AP8.6 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?

x(1) u(t) FIGURE AP8.6 Suspended spring-mass system with parameters k and b.