Question

Do each of the following eight (8) problems. The problems have equal weight. For each problem, in order to receive maximum possible credit, show the steps of the solution clearly,and provide appropriate explanation. Return this exam with your answer sheets . Chapter continunous-time system, with time t in seconds () input fO, and output yo. is specified by the equation y(t) = 1.5cos(2x500 + 0.8ft). a. Is this system instantaneous (memoryless) or dynamic (with memory)? Justify your answer Show that the system fails to satisfy the homogeneity or scaling property required for explain your work b. superposition to hold for inputs fi(0)-2.0 and (O)-3i()-6.0. Clearly show and 2. (Chapter 2). A linear, time-invariant, continuous-time (LTIC) system with input ft) and output y(t) is specified by the differential equation a. Find the characteristic polynomial, characteristic equation, characteristic root(s), and characteristic mode(s) of this system. b. Is this system asymptotically stable, marginally stable, or unstable? Justify your answer. 3. (Chapter 2), Let ho)-uO and fro-2u't-2), Let yo-ho t0. Here, u) is the unit step unction, and the Use direct integration to compute y(3). Clearly show your work. Sketches may help. (Chapter 9). A linear, time-invariant, discrete-time (LTID, time index k) system with input ” means convolution. 4. fIk] and output y[k] is specified by the difference equation (in delay form) a. Use the iterative solution technique (that is, marching) to find the values of system unit impulse response h[k] for k -0,1. Clearly show your steps b. Is the system asymptotically stable, marginally stable, or unstable? Justify your answer. (Continued on next page)

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