2.26 Figure P2.26a shows a schematic diagram of an optical disk drive system. The spindle motor (contained in the chassis) rotates the disk and the cart motor translates the pick-up head (PUH) along the radial direction of the spinning disk so that the focused laser "reads" the desired data track on the optical disk. Note that although the cart servo motor can position the cart in the radial direction, the cart is rigidly attached to the chassis (see Reference 4 for additional details). Figure P2.26b shows the optical disk drive as a simplified two-mass mechanical system. The PUH mass m, is connected to the cart with stiffness k₁ and friction coefficient b₁, while the chassis and cart are lumped into mass m₂. A series of rubber mounts connects the chassis mass m₂ to the frame and these mounts have lumped stiffness k₂ and friction coefficient by. The mounts are used to suppress transmitted vibrations from the motion of the frame. The absolute displacements (as measured from the static equilibrium position) of the PUH and chassis/cart are x₁ and X2, respectively. The absolute displacement of the frame is x(t). Derive the mathematical model of the optical disk drive system. k₂ C Cart Radial direction Disk Laser Pick-up Rubber vibration isolation mounts Figure P2.26a Frame Xin() b₁ Vibration isolation mounts Figure P2.26b www H head. (PUH) Disk rotation Spindle motor Chassis Cart servo motor Frame Chassis/cart www b₁ m2 Pick-up head (PUH)