New to Physics Forums? Struggling with Laplace?

[awaheed]

hi everyone, I am new to physics forums and am struggling with Laplace.

I have been given 3 problems:

a) sint-tcost -> find the laplace transform of the fiven function without using table

b) 3/ s2(s2-a) -> Find the inverse laplace transform of the given function

c) Ln (1 + sinx) -> find from first principles the first three non zero terms of the maclaurin series of the given function f(x)

Any help would be appreciated :)

 

[jjmontero9]

Hi ! Without using the table means that you need to apply the integral definition.
The Laplace Transform of any function is calculated by integrating this way:

$$\mathcal{L} \left\{ f(t) \right\} = \int_{0}^{+\infty}{f(t)\cdot{}e^{-s\cdot{}t}dt}$$

Where f(t) is the original function.
And the inverse transform is calculated as:

$$\mathcal{L}^{-1} \left\{ F(s) \right\} = \frac{1}{2\pi{}i}\int_{\sigma-i\infty}^{\sigma+i\infty}{F(s)\cdot{}e^{s\cdot{}t}ds}$$

And for the third one, Maclaurin means you're looking for the Taylor expansion centered at 0.

 

[Integral]

Please show us some of what you have done.