Question

The output of a linear system to unit step input u (t) is t² e^2t. The system function H(s) is
1. \(\frac{2}{s^2(s+2)}\)
2. \(\frac{s}{(s+2)^2}\)
3. \(\frac{2}{(s+2)^3}\)
4. \(\frac{2s}{(s+2)^3}\)

Answer 1

Correct Answer - Option 4 : \(\frac{2s}{(s+2)^3}\)

Concept:

Output of a system Y(s) = Input X(s) × Transfer function H(s)

\(L\left\{ {{t^n}} \right\} = \frac{{n!}}{{{s^{n + 1}}}}\)

Analysis:

y(t) = t2 e^2t

\(Y(s) = \frac{2}{(s+2)^3}\)

x(t) = u(t)

\(X(s) = \frac{1}{s}\)

Y(s) = X(s) × H(s)

\(H(s) = \frac{Y(s)}{X(s)}\)

\(= \frac{2s}{(s+2)^3}\)