A machine, largely made of aluminum, is modeled as a simple mass (of 100 kg) attached to ground through a spring of 2000 N>m. The machine is subjected to a 100-N harmonic force at 20 rad>s. Design an undamped tuned absorber system (i.e., calculate ma and ka ) so that the machine is stationary at steady state. Aluminum, of course, is not completely undamped and has internal damping that gives rise to a damping ratio of about ζ = 0.001.

Similarly, the steel spring for the absorber gives rise to internal damping of about ζa = 0.0015.

Calculate how much this spoils the absorber design by determining the magnitude X using equation (5.32).