The response of the liquid level in a tank is given by the first-order differential equation: A \frac{d h(t)}{d t}=q_{0}(t) where h(t) is the level in the tank in m,

gdt) is the flow of the liquid into the tank in m/s, and A =0.5 m is the constant area of the tank in m2. \text { Obtain the transfer function for the tank, } G(s)=\frac{H(s)}{Q_{0}(s)} Assume that initially the valve of the inlet stream was completely closed and the level in thetank was h(0) = 0.25 m. At t = 0, the valve was opened, and the flowrate was maintained atgo(0) = 0.25 m/min. Knowing that the height of the tank is 3.5 m, after which the tank willoverflow. Determine the time needed to fill up the tank. O Simulate and plot the responses obtained in parts (b) and (c). \text { Obtain the response of the level to a unit step in flow, } q_{o}(t)=u(t) .