Question

Which of the following types of standard input signals has the Laplace transformation as \(\frac{\omega}{(s^2 + \omega^2)}\) ?
1. Cosine type of signal
2. Unit impulse signal
3. Sinusoidal type signal
4. Parabolic type signal

Answer 1

Correct Answer - Option 3 : Sinusoidal type signal

Concept:

Some important Laplace transforms are:

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

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

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

\(L\left\{ {\cos \omega t} \right\} = \frac{s}{{{s^2} + {\omega ^2}}}\)

\(L\left\{ {\sin \left( {{\omega }t} \right)} \right\} = \frac{\omega }{{{s^2} + {{\omega}^2}}}\)