A DVD drive is mounted on a chassis and is modeled as a single-degree-of-freedom spring, mass, and damper. During normal operation, the drive (having a mass of 0.4 kg) is subject to a harmonic force of 1 N at 10 rad/s.
Because of material considerations and static deflection, the stiffness is fixed at 500 N/m and the natural damping in the system is 10 kg/s.
The DVD player starts and stops during its normal operation providing initial conditions to the module of x0 = 0.001 m and 0 = 0.5 m/s. The DVD drive must not have an amplitude of vibration larger then 0.008 m even during the transient stage. First, compute the response by numerical simulation to see if the constraint is satisfied.
If the constraint is not satisfied, find the smallest value of damping that will keep the deflection less than 0.008 m.