In the liquid level system, the deviation in flow rate to the first tank an impulse of magnitude $5.$ The

following data apply; $A_1=1,A_2=A_3=2,R_1=1,R_2=1\mathrm{.}5$ and $q_1=\frac{h_1^{0\mathrm{.}5}}{R_1},q_2$ is linear, $h_{1s}=2.$

a$)$ Determine the expression for h$\text{'}1(s),h_2^{\text{'}}(s),h_3(s).$

b$)$ Determine the maximum level in three of the tanks from the ultimate steady state value and time at

which each maximum occurs.

c$)$ Determine h$\text{'}1(3\mathrm{.}5),$ h$\text{'}2(3\mathrm{.}5),$ h$\text{'}3(3\mathrm{.}5).$ For h$\text{'}2$ and h$\text{'}3,$ use graphs after first finding the values of $$

and $$ for an equivalent second order.