GATE EE 2020 Set 1 — Question 20
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Signals & Systems → Laplace & Z Transforms → Transfer Function & Pole-Zero
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Question
Consider a linear time-invariant system whose input and output are related by the following differential equation:The poles of this system are at
Correct answer
(A) +2j,-2j
Solution
The given differential equation is:To find the poles of the system, we take the Laplace transform of the differential equation, assuming zero initial conditions:
Factor out :
The transfer function is defined as the ratio of the output Laplace transform to the input Laplace transform:
The poles of the system are the values of that make the denominator of the transfer function equal to zero:
Thus, the poles of the system are and .The final answer is
Factor out :
The transfer function is defined as the ratio of the output Laplace transform to the input Laplace transform:
The poles of the system are the values of that make the denominator of the transfer function equal to zero:
Thus, the poles of the system are and .The final answer is
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