Question

Find the poles of transfer function which is defined by input x(t)=5Sin(t)-u(t) and output y(t)=Cos(t)-u(t).

(a) 4.79, 0.208

(b) 5.73, 0.31

(c) 5.89, 0.208

(d) 5.49, 0.308

This question was addressed to me in my homework.

The doubt is from Laplace Transform by Properties in division Laplace Transform of Engineering Mathematics

Answer 1

The correct answer is (a) 4.79, 0.208

Best explanation: Given ,y(t)=Cos(t) – u(t) and x(t) = 5Sin(t) – u(t),

Hence, transfer function H(s)=\(\frac{[\frac{s}{s^2+1}-\frac{1}{s}]}{[\frac{5}{s^2+1}-\frac{1}{s}]} =-\frac{1}{\frac{s(s^2+1)}{\frac{(5s-s^2-1)}{s(s^2+1)}}}=\frac{1}{S^2-5S+1}\)

Roots of equation s^2 – 5s + 1 = 0 is s = 4.79, 0.208.