Electrical Engineering > GATE 2020 > System Properties
Consider a linear time-invariant system whose input r(t) and output y(t) are related by the following differential equation:
d2y(t)/dt2+4y(t)=6r(t)
The poles of this system are at
d2y(t)/dt2+4y(t)=6r(t)
The poles of this system are at
Correct : a
The correct answer is Option A: +2j, -2j.
To find the poles, take the Laplace transform of the given differential equation (assuming zero initial conditions):
d2y(t)/dt2 + 4y(t) = 6r(t)
becomes
s2Y(s) + 4Y(s) = 6R(s)
So the transfer function is:
H(s) = Y(s)/R(s) = 6 / (s2 + 4)
Poles are the roots of the denominator s2 + 4 = 0 ⇒ s2 = -4 ⇒ s = ±2j.
Since both poles lie on the imaginary axis, the system is marginally stable and produces a sustained sinusoidal output.
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