The water level h{t) in a tank is controlled by an open-loop system, as shown in Figure P2.47. A DC motor controlled by an armature current i, turns a shaft, opening a valve. The inductance of the DC motor is negligible, that is, La = 0. Also, the rotational friction of the motor shaft and valve is negligible, that is, b = 0. The height of the water in the tank is given by: H(s)=(1.6/(s+1))e(s). And the motor constant is K.=K=10, and the inertia of the motor shaft and valve is J-6 *10 kgm². Determine (a) the differential equation for input v(t) and output h(t) and (b) the transfer function H(s)/V(s). Amplifier 213 M