The water level h(t) in a tank is controlled by an open-loop system, as shown below. A DC motor controlled by an armature current i, turns a shaft, opening a valve. The inductance of the DC motor is negligible, L. = 0 and the rotational friction of the motor shaft and valve is negligible, b = 0. The height of the water tank is h(t)= [1.60(t)-h(t)]dt, the motor constant is Km 10, and the inertia of the motor shaft is J = 6 x 103 kg m2. Determine the (a) the differentital equation for h(t) and v(t) and (b) the transfer function H(s)/V(s) Amplifier + A-50 0 Valve Motor 800 (1)