Question

Laplace transform of cos(ωt) is
1. \(\frac{s}{{{s^2} + {\omega ^2}}}\)
2. \(\frac{\omega }{{{s^2} + {\omega ^2}}}\)
3. \(\frac{s}{{{s^2} - {\omega ^2}}}\)
4. \(\frac{\omega }{{{s^2} - {\omega ^2}}}\)

Answer 1

Correct Answer - Option 1 : \(\frac{s}{{{s^2} + {\omega ^2}}}\)

Concept:

Some important Laplace transforms are:

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

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

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

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

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