# Operate the Laplace Transform on the following text{(i) } f(t)=cos(3t) text{(ii) } f(t)=t^{frac{1}{2}}

Operate the Laplace Transform on the following

You can still ask an expert for help

## Want to know more about Laplace transform?

• Questions are typically answered in as fast as 30 minutes

Solve your problem for the price of one coffee

• Math expert for every subject
• Pay only if we can solve it

estenutC
$\text{Step 1}$

$L\left\{\mathrm{cos}\left(3t\right)\right\}=\frac{{s}^{2}}{{s}^{2}+{3}^{2}}$
$=\frac{{s}^{2}}{{s}^{2}+9}$

$\text{Step 2}$

$L\left\{f\left(t\right)\right\}=L\left\{{t}^{\frac{1}{2}}\right\}$
$\text{using the formula}L\left\{{t}^{n-\frac{1}{2}}\right\}=\frac{\left(2n-1\right)!\sqrt{\pi }}{{2}^{n}s\frac{n+1}{2}}$

$L\left\{{t}^{1-\frac{1}{2}}\right\}=\frac{\left(2\left(1\right)-1\right)!\sqrt{\pi }}{{2}^{1}{s}^{n+\frac{1}{2}}}$
$=\frac{\left(1\right)!\sqrt{\pi }}{2{s}^{1+\frac{1}{2}}}$
$=\frac{\left(1\right)!\sqrt{\pi }}{2{s}^{\frac{3}{2}}}$
$=\frac{\sqrt{\pi }}{2{s}^{\frac{3}{2}}}$