2. Consider the system shown below. flow Lake 8.(t) R3 G(s) = C (a) [8 marks] Find the transfer function Q(s)/Qo(s). Your solution must remain within the hydraulic domain (i.e., do not transform the hydraulic system into another domain). (b) [1 mark] Provide a brief logical argument for why the transfer function you obtained in part (a) is at least plausibly correct. (Alternatively, provide a brief logical argument for why the transfer function you obtained in part (a) cannot possibly be correct.) (c) [2 marks] Suppose you obtained the following transfer function in part (a): Q(s) 1 Qo(s) (s+ 100) (s + a) = g(t) for some parameter a > 0. [Note that this is not actually the answer to part (a)]. Suppose the input signal is a unit step (i.e., Qo(s) = 1/s). Find an expression for q (t) as a function of the parameter a.