FOLLOWING SIGNAL is GIVEN as:\(u\left( t \right) \LEFTRIGHTARROW \frac{1}{s}\;{R_e}\left\{ s \right\} > - a\)\(\frac{{{t^{n - 1}}}}{{\left( {n - 1} \right)!}}{e^{ - at}}u\left( t \right) \leftrightarrow \frac{1}{{{{\left( {s + a} \right)}^n}}}{R_e}\left\{ s \right\} > - a\)Calculation:Given:R(t) = u(t)C(t) = t2 e-2t\(R\left( s \right) = \frac{1}{s}\) \({t^2}{e^{ - 2t}}u\left( t \right) \leftrightarrow \frac{2}{{{{\left( {s + 2} \right)}^3}}}\) \(H\left( s \right) = \frac{{C\left( s \right)}}{{R\left( s \right)}} = \frac{{\frac{2}{{{{\left( {s + 2} \right)}^3}}}}}{{\frac{1}{s}}}\)\(H\left( s \right) = \frac{{2s}}{{\left( {s + 2} \right)3}}\)