Question

Laplace transform for the function $f\left(x\right)=\cos h\left(ax\right)$ is

• A. $\frac{a}{s^2-a^2}$
• B. $\frac{s}{s^2-a^2}$
• C. $\frac{a}{s^2+a^2}$
• D. $\frac{s}{s^2+a^2}$

Answer 1

The correct option is B $\frac{s}{s^2-a^2}$

we know that
$\cos h\left(ax\right)=\frac{e^{ax}+e^{-ax}}{2}$
Taking Laplace transform, we get,
$F\left(s\right)=\frac{1}{2}L\left\{e^{ax}\right\}+\frac{1}{2}L\left\{e^{-ax}\right\}$
$=\frac{1}{2}[\frac{1}{s-a}+\frac{1}{s+a}]$
$=\frac{2s}{2(s^2-a^2)}$
$=\frac{s}{s^2-a^2}$