Question

The step response of system has Laplace transform of Y(s)= 8/s(s+2)(s2+4s+8). Please find its time-domain response function y(t) using partial fraction expansion.

Answer 1

To find the time-domain response function y(t), we need to use partial fraction expansion to break down the Laplace transform expression of Y(s) into simpler fractions. Using algebraic manipulations and comparing coefficients, we can determine the values of the constants and then take the inverse Laplace transform to obtain y(t).

Step-by-step explanation:

To find the time-domain response function y(t), we need to use partial fraction expansion to break down the Laplace transform expression of Y(s) into simpler fractions. Starting with the expression Y(s) = 8/(s(s+2)(s^2+4s+8)), we first factor the denominator to s(s+2)(s+2+j2)(s+2-j2). Next, we use partial fraction decomposition to write the expression as A/s + B/(s+2) + (Cs+D)/(s^2+4s+8), where A, B, C, and D are constants.

Using algebraic manipulations and comparing coefficients, we can determine the values of A, B, C, and D. Once we have these values, we can take the inverse Laplace transform to obtain the time-domain response function y(t)