Question

Find the poles of transfer function given by system ^d^2⁄dt^2 y(t) – ^d⁄dt y(t) + y(t) – ∫0^t x(t)dt = x(t).

(a) 0, 0.7 ± 0.466

(b) 0, 2.5 ± 0.866

(c) 0, 0 .5 ± 0.866

(d) 0, 1.5 ± 0.876

I had been asked this question during an online interview.

The above asked question is from Laplace Transform by Properties in chapter Laplace Transform of Engineering Mathematics

Answer 1

Correct choice is (c) 0, 0 .5 ± 0.866

Explanation: We know that,

Given, \(\frac{d^2}{dt^2} y(t)-\frac{d}{dt} y(t)+y(t)-\int_0^t x(t)dt=x(t)\)

Now, Taking laplace, we get, \((s^2-s+1)Y(s)=(1+\frac{1}{s})X(s)\)

H(s)=\(\frac{s+1}{s(s^2-s+1)}\)

Roots of s^3-s^2+s=0, are 0,.5±0.866