226k views
1 vote
Find the unit impulse response of the system specified by the following equation.

a) H(s) = 1/s
b) H(s) = s/(s² + 1)
c) H(s) = e^(-2s)
d) H(s) = 1/(s + 3)

User Adaam
by
8.2k points

1 Answer

6 votes

Final answer:

The unit impulse responses of the given system equations are: a) u(t), b) e^(-it) + e^(it), c) e^(-2t), d) e^(-3t).

Step-by-step explanation:

To find the unit impulse response of a system, we need to find the inverse Laplace transform of the transfer function. Let's go through each option:

a) H(s) = 1/s

The inverse Laplace transform of 1/s is the unit step function, u(t).

b) H(s) = s/(s² + 1)

Using partial fraction decomposition, we can write the transfer function as H(s) = 1/(s + i) + 1/(s - i), where i is the imaginary unit. The inverse Laplace transform of 1/(s + i) is e^(-it), and the inverse Laplace transform of 1/(s - i) is e^(it). Therefore, the unit impulse response is e^(-it) + e^(it).

c) H(s) = e^(-2s)

The inverse Laplace transform of e^(-2s) is the unit impulse function scaled by a factor of e^(-2t), where t is the time variable. Therefore, the unit impulse response is e^(-2t).

d) H(s) = 1/(s + 3)

The inverse Laplace transform of 1/(s + 3) is e^(-3t). Therefore, the unit impulse response is e^(-3t).

User Christian Lindig
by
9.0k points

No related questions found

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