= w1 = Two tanks are connected together in the following unusual way. The density of the incoming liquid, p= 1kg/m, is constant. The cross- sectional areas of the two tanks are Al 10m2 and A2 = 5m. W2 is positive for flow from Tank 1 to Tank 2. The two valves are linear with resistances R2 0.98 and R3 0.49 Assume that the acceleration due to gravity is, g 9.8m/ s2 and that all initial conditions are zero. = hi h2 ..m S.m W3- (a) Find the Laplace transforms of the model equations and derive an expression for H(s) and H2(s) in terms of independent variables. (b) Using partial fraction expansion find the inverse Laplace transforms of H1(s) for the following changes in wi(t) and plot hi(t). (i) A step change, i.e., w1(t) = S(t) (ii) An impulse change, i.e., wi(t) = (t) (iii) A sinusoidal change of frequency w = 1rad/ s, i.e., w1(t) = sin(t) - =