1) The simplified model of an insulin pump shown below, consists of a small DC motor connected to a rack and pinion, the end of which is attached to the plunger of a syringe of insulin. When a current i(t) is applied to the motor windings, the motor generates a torque r(t) where, t(t) = K,i(t) The torque is converted in to the forcef (t), by the rack and pinion such that T(t) f(t) = R where R is the effective radius of the wheel. The entire mass of the system can be regarded as the equivalent lumped mass M. The syringe plunger has an associated viscous fraction of B and equivalent spring constant of K. a) Determine the differential equation which relates y(t)( the displacement of the syringe plunger ) to the applied current i(t). (20%)