The movable arm with read/write head of a disk drive unit is modeled as a simple oscillator. The unit has an equivalent bending stiffness k = 10 dyne · cm/rad and damping constant b. An equivalent rotation u(t) radians is imparted at the read/write head. This in turn produces a (bending) moment to the read/write arm, which has an equivalent moment of inertia J = 1 × 10-3 gm · cm2, and bends the unit at an equivalent angle θ about the centroid.
(a) Write the input-output differential equation of motion for the read/write arm unit.
(b) What is the undamped natural frequency of the unit in rad/s?
(c) Determine the value of b for 5% critical damping.
(d) Write the frequency transfer function of the model.