A process is perturbed by a sinusoidally varying input, u(t), whose amplitude is A and whose frequency is w. The resulting process output relation is given by

(a) What must have been the differential equation representing the process? The initial condition

(b) Find y(t).

(c) Plot the input sinusoid and your result, y(t), on the same graph. What can you say about their relation as t becomes large? For part (c), consider both: (i) the amplitude of output relative to that of the input and (ii) the angular shift between the periodic component of each signal as measured in either radians, degrees, or fraction of a full cycle (2? radians = 360^o = 1 cycle). Is either of these two relations a function of the value of the input forcing frequency w?

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