Problem $3.(35$ pts$)$ In the system of three tanks in

series shown in Figure $2,$ the outlet flow rate from

the third tank $F_{\text{o}\text{u}\text{t}}$ is set by a pump that has been

installed, and is independent of the liquid level in the

tank$.$ Derive the transfer function of the system with

$F_{in}$ as input and $h_3$ as output. If the system is initially

at steady state but at time $t=0,$ Fin undergoes a

step change of size M$,$ calculate the response of $h_3.$

What will happen as $t?$

Figure $2$