Question

Find the equation of transfer function which is defined by y(t)-∫0^t y(t)dt + ^d⁄dt x(t) – 5Sin(t) = 0.

(a) \(\frac{s(e^{-as}-1)}{s-1}\)

(b) \(\frac{(e^{-as}-s)}{s-1}\)

(c) \(\frac{s(e^{-as}-s)}{s-1}\)

(d) \(\frac{s(e^{-as}-s^2)}{s-1}\)

This question was addressed to me in examination.

My question is taken from Laplace Transform by Properties in division Laplace Transform of Engineering Mathematics

Answer 1

Right option is (c) \(\frac{s(e^{-as}-s)}{s-1}\)

To explain I would say: Given, \(y(t)-∫_0^t y(t)dt+\frac{d}{dt} x(t)-x(t-a)=0\)

Taking Laplace, \(Y(s)-\frac{Y(s)}{s}+sX(s)-e^{-as} X(s)=0\)

H(s)=Y(s)/X(s) =\(\frac{(e^{-as}-s)}{1-\frac{1}{s}}=\frac{s(e^{-as}-s)}{s-1}\)