42.4k views
4 votes
Determine the system response y(t) for an LTI system, if H(s) = 2/(s² + 3s + 2)?

1 Answer

4 votes

Final answer:

The system response y(t) is the inverse Laplace transform of the transfer function H(s). For H(s) = 2/(s² + 3s + 2), the response is y(t) = 2e-t - 2e-2t, which is the impulse response of the system.

Step-by-step explanation:

To determine the system response y(t) for an LTI system with the transfer function H(s) = 2/(s² + 3s + 2), we start by finding the inverse Laplace transform of H(s). This will give us the impulse response h(t) of the system. The poles of H(s) are the roots of the denominator s² + 3s + 2, which factorizes to (s + 1)(s + 2).

Therefore, the partial fraction decomposition of H(s) is:

H(s) = 2/((s+1)(s+2)) = A/(s+1) + B/(s+2)

By finding the values of A and B, we can determine the inverse Laplace of each term individually. After finding A and B, we get:

H(s) = 2/(s+1) - 2/(s+2)

The inverse Laplace transform gives us the impulse response:

h(t) = 2e-t - 2e-2t

This impulse response h(t) represents the system response y(t) to a delta function input. If the input were something other than a delta function, you would need to convolve this impulse response with the actual input to get the output y(t).

User Brpyne
by
7.6k points
Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories