Question

Laplace Transform :
f(t) = a sin pt \(0 11 years ago

Answer 1

can i do this :
\(\Large \int \limits_0^{\pi/p}a \sin (pt) e^{-st} dt +\int \limits _{\pi/p}^{2\pi/p}0 dt\)

Answer 2

@mathmale @ganeshie8 @SithsAndGiggles

Answer 3

if i do that, i get
\(\Large \dfrac{ap}{(p^2+s^2 ) }(1+e^{(-sπ/p)} )\)

but i am not sure whether i can split those 2 integrals like i did.
If what i did is correct, can someone verify whether my final answer is correct ?

Answer 4

Ok, what u did there is right so far. Did the question mention anything about that being a periodic pulse? Because then if you take f(x) to be the \[\frac{ 2\pi }{p }\] - periodic extension of fx(s) then your answer would become: \[\frac{ ap(1+e ^{-s \pi/p}) }{ p ^{2}+s ^{2}(1+e ^{-2s \pi/p}) }\]

Answer 5

f(t) = f(t+2π/p)

implies f(t) is periodic with period 2π/p

Answer 6

so my final answer would be
\(\Large \dfrac{ ap(1+e ^{-s \pi/p}) }{ (p ^{2}+s ^{2})(1+e ^{-2s \pi/p}) }\)
???

Answer 7

yep thats right

Answer 8

thanks Tushara :)

Answer 9

no worries

Answer 10

oh, isn't it
\(\Large \dfrac{ ap(1+e ^{-s \pi/p}) }{ (p ^{2}+s ^{2})(1-e ^{-2s \pi/p}) }\)

and the final answer be
\(\Large \dfrac{ ap }{ (p ^{2}+s ^{2})(1-e ^{-s \pi/p}) }\)

instead ?

Answer 11

no, the first one is right, from how i remember doing it. Take a look at example 4 on page 4 at
http://www.math.vt.edu/people/dlr/m2k_opm_lapper1.pdf
that will justify ur answer

Answer 12

i have to multiply by
\(\Large \dfrac{1}{1-e^{-Ts}}\)
right ???

Answer 13

for 1st one, there is 1\(\huge +\) ... in the denominator

Answer 14

I'm curious if writing \(f(t)\) as a Fourier series might be another method...

Answer 15

writing it as fourier series and then using s= jw ?

Answer 16

Sorry I'm not sure what you mean by that

Answer 17

hah, nothing.
Fourier Transform to Laplace transform, we probably put s=jw....but nvm..

anyways my updated final answer is correct ?

Answer 18

Oh, I see what you mean. \(j=\sqrt{-1}\), right? I'm used to using \(i\). That might work too, but I'm not sure.

Answer 19

yes that.
and i have lots of other fourier series examples to solve, so i will not be trying this :P

Answer 20

i still think
\(\Large \dfrac{ ap }{ (p ^{2}+s ^{2})(1-e ^{-s \pi/p}) }\)
should be correct final answer...

Answer 21

Yeah I'm inclined to agree.

Answer 22

thanks! :D