Question

The system given by equation 5 ^d^3⁄dt^3 y(t) + 10 ^d⁄dt y(t) – 5y(t) = x(t) + ∫0^t x(t)dt, is?

(a) Stable

(b) Unstable

(c) Has poles 0, 0.455, -0.236±1.567

(d) Has zeros 0, 0.455, -0.226±1.467

The question was asked in unit test.

My question is based upon Laplace Transform by Properties topic in chapter Laplace Transform of Engineering Mathematics

Answer 1

The correct option is (a) Stable

To elaborate: Given, 5 ^d^3⁄dt^3 y(t) + 10 ^d⁄dt y(t) – 5y(t) = x(t) + ∫0^t x(t)dt,

By laplace transform, 5s^3 Y(s)+10sY(s)-5Y(s)=X(s)+1/s X(s)

Hence,

\(\frac{Y(s)}{X(s)} =\frac{[1+1/s]}{5s^3+10s-5}=\frac{[s+1]}{s(5s^3+10s-5)}\)

Poles of \(\frac{Y(s)}{X(s)}\) are, 0 ,0.455,-0.226±1.467

Hence system is Unstable.