enrosca0fx

## Answered question

2023-01-03

What is the Laplace transform of $t\mathrm{cos}t$ into the s domain?

### Answer & Explanation

Gary Montoya

Beginner2023-01-04Added 9 answers

A function of t, f(t), is transformed into a new function of s, F, by a Laplace transformation (s). That is indicated as:
$ℒ\left[f\left(t\right)\right]=F\left(s\right)$
where the actual transform can be acquired from a table of Laplace transforms.
For $f\left(t\right)=t\mathrm{cos}\left(at\right)$:
$ℒ\left[f\left(t\right)\right]=ℒ\left[t\mathrm{cos}\left(at\right)\right]=\frac{{s}^{2}-{a}^{2}}{{\left({s}^{2}+{a}^{2}\right)}^{2}}$
Then, for your function, plug in a=1 to get:
$ℒ\left[f\left(t\right)\right]=ℒ\left[t\mathrm{cos}t\right]=\frac{{s}^{2}-{1}^{2}}{{\left({s}^{2}+{1}^{2}\right)}^{2}}$
$=\frac{{s}^{2}-1}{{\left({s}^{2}+1\right)}^{2}}$

Do you have a similar question?

Recalculate according to your conditions!

Ask your question.
Get an expert answer.

Let our experts help you. Answer in as fast as 15 minutes.

Didn't find what you were looking for?