A liquid storage system is shown below. The normal operating conditions are q1= 10ft3/min,q2=5ft3/min,h=4ft. The tank is 6ft in diameter, and the density of each stream is 60lb/ft3. Suppose that a pulse change in q1 occurs as shown in the figure. (a) What is the transfer function relating H to Q1 (b) Derive an expression for h(t) for this input change. (c) What is the new steady-state value of liquid level h ? (d) Repeat (b) and (c) for the sinusoidal input (3sin(2t)) and doublet pulse input (same in Question 1) where the changes in q1 are from 10 to 15 to 5 to 10 ft3/min