[amp_mcq option1=”u(t) – 2e-t u(t) + e-3t u(t)” option2=”2u(t)” option3=”u(t)” option4=”2u(t) – 2e-t u(t) + e-3t u(t)” correct=”option1″]<\/p>\n
The correct answer is $\\boxed{\\text{A. }u(t) – 2e^{-t}u(t) + e^{-3t}u(t)}$.<\/p>\n
The forced response of a system is the response of the system to a step input. The step input is a function that is zero for all time before $t=0$ and is equal to one for all time after $t=0$. The forced response of a system can be found by taking the Laplace transform of the step input and dividing by the Laplace transform of the system’s transfer function.<\/p>\n
The Laplace transform of the step input is $1$. The Laplace transform of the system’s transfer function is $G(s) = \\frac{3-s}{(s+1)(s+3)}$. Therefore, the forced response of the system is<\/p>\n
$$Y_f(s) = \\frac{1}{s} \\cdot \\frac{3-s}{(s+1)(s+3)} = \\frac{3-s}{s(s+1)(s+3)}$$<\/p>\n
We can find the forced response in the time domain by taking the inverse Laplace transform of $Y_f(s)$. The inverse Laplace transform of $\\frac{3-s}{s(s+1)(s+3)}$ is<\/p>\n
$$Y_f(t) = u(t) – 2e^{-t}u(t) + e^{-3t}u(t)$$<\/p>\n
Therefore, the forced response of the system is $u(t) – 2e^{-t}u(t) + e^{-3t}u(t)$.<\/p>\n
The other options are incorrect because they do not match the forced response of the system.<\/p>\n","protected":false},"excerpt":{"rendered":"
[amp_mcq option1=”u(t) – 2e-t u(t) + e-3t u(t)” option2=”2u(t)” option3=”u(t)” option4=”2u(t) – 2e-t u(t) + e-3t u(t)” correct=”option1″]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[959],"tags":[],"class_list":["post-51024","post","type-post","status-publish","format-standard","hentry","category-signal-processing","no-featured-image-padding"],"yoast_head":"\n