Laplace transform of cos (ωt) is $$\frac{{\text{s}}}{{{{\text{s}}^2} + {\omega ^2}}}.$$  The Laplace transform of e-2t cos(4t) is

Laplace transform of cos (ωt) is $$\frac{{\text{s}}}{{{{\text{s}}^2} + {\omega ^2}}}.$$  The Laplace transform of e-2t cos(4t) is Correct Answer $$\frac{{{\text{s}} + 2}}{{{{\left( {{\text{s}} + 2} \right)}^2} + 16}}$$

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Laplace transform of the function f(t) is given by $${\text{F}}\left( {\text{s}} \right) = {\text{L}}\left\{ {{\text{f}}\left( {\text{t}} \right)} \right\} = \int_0^\infty {{\text{f}}\left( {\text{t}} \right){{\text{e}}^{ - {\text{st}}}}{\text{dt}}{\text{.}}} $$       Laplace transform of the function shown below is given by
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Two monochromatic waves having frequencies $$\omega $$ and $$\omega + \Delta \omega \left( {\Delta \omega \ll \omega } \right)$$    and corresponding wavelengths $$\lambda $$ and $$\lambda - \Delta \lambda \left( {\Delta \lambda \ll \lambda } \right)$$    of same polarization, travelling along X-axis are superimposed on each other. The phase velocity and group velocity of the resultant wave are respectively given by
If the Laplace transform of $${{\text{e}}^{\omega {\text{t}}}}$$  is $$\frac{1}{{{\text{s}} - \omega }},$$  the Laplace transform of tcosh t is