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An LTI system is defined by the equation (+5+6)()=(+1)() (a) Find the characteristic equation, characteristic roots, and characteristic modes of this system (b) Comment on the stability of the system. (c) Find yo(t), the zero-input component of the response for t0, if the initial conditions are y0(0) = 2 and (0) = -1 (d) Mathematically derive an expression for h(t), the impulse response of the system. (e) Using the convolution tables and the result of part (d), find the zero-state output for the system given the input x(t) = e-3tu(t) (f) What is the total system response based on the conditions and input specified above? (g) What is the natural response and what is the forced response of this system? (h) Using Matlab, plot the impulse and step responses and frequency response (magnitude and phase) of this system directly from the differential equation. Hint: The sample code given in Module 6 may be used, but the frequency range will have to be increased. (1) Compare the impulse response plot from part (h) to the expression from part (d). Comment on the overall shape and specific points on the plot that confirm that they are equivalent. (1) Using the frequency response plots from part (h), determine the output of the system if x(t) = 8 - 10 cos(t-200) - 6 cos(30t-300)