Chapter 6, Problem 49P

The read/write head assembly arm of a computer hard disk drive (HDD) can be modeled as a rigid rotating body with inertia I_b. Its dynamics can be described with the transfer function

$P\left(s\right)=\frac{X\left(s\right)}{F\left(s\right)}=\frac{1}{I_b{s}^2}$

where X(s) is the displacement of the read/write head and F(s) is the applied force (Yan, 2003). Show that if the HDD is controlled in the configuration shown in Figure P6.11, the arm will oscillate and cannot be positioned with any precision over a HDD track. Find the oscillation frequency.