2. An LTI system is described by the following linear constant-coefficient differential equation. Its input is x(t) = cos (wt). d²y dy dx +2+ 7y = 5- dt dt? dt a. If w = 2 rad/sec, compute the output y(t). b. Find the frequency w so that y(t) = A cos(wt) for some constant A > 0. That is, the input W SC and output sinusoids are in phase.

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2. An LTI system is described by the following linear constant-coefficient differential equation. Its
input is x(t) = cos (wt).
d²y
dy
dx
+2-
+ 7y = 5
dt
dt2
dt
a. If w = 2 rad/sec, compute the output y(t).
b. Find the frequency w so that y(t) = A cos(wt) for some constant A > 0. That is, the input
and output sinusoids are in phase.
Transcribed Image Text:2. An LTI system is described by the following linear constant-coefficient differential equation. Its input is x(t) = cos (wt). d²y dy dx +2- + 7y = 5 dt dt2 dt a. If w = 2 rad/sec, compute the output y(t). b. Find the frequency w so that y(t) = A cos(wt) for some constant A > 0. That is, the input and output sinusoids are in phase.
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