Consider the system from Problem and input u. Fix t = 1.5 and draw h(1.5-7) and u(7) versus 7 [0, 1.5]. Also sketch the product and note that area under the product is equal to hu when t = 1.5. All three sketches can be put in the same figure. Now, in a new figure, sketch h(7) and u(1.5-7) versus 7 E [0, 1.5]. Also sketch the product and note that the area under the product is equal to uh when t = 1.5. This simple example should give you some insight into why hu= u* h. Consider the first order ODE = -y+2u. The solution to the initial value problem is given by y(t) = ety(0) + ) + h(t - T)u(T)dT, where the function h is h(t)=2e, t0 Let the initial condition in this analysis be 0, i.e. y(0) = 0. Answer the following: 1. Compute y for t 0 using (1) for the following inputs: u = 1, t0 1 t [0,1] U2 = 10 t>1 e-t t = [0, 1] 13 = -0.5 t (1,2] t>2 Graphs of the different inputs are shown below: 05 D -0.5 - 0.5 4.5 andus 05 05 (1) -15 0.5 1 1.5 2 25 3 3.5 4 D 0.5 1.5 2 25 3 3.5 4 D 0.5 1 1.5 2 25 3 35 4 Time() Time() Time()