Laplace transform Definition and 779 Threads

L is Laplace Transform operator. Question is: Let f(t) = t^2. Derive L[f] from L[1] So I know f(1) =1 and L[1] = \frac{1}{s} Carrying out the Transform... L[f] = \int_{0}^{\infty} e^{-st}t^2 dt Integration by parts u = t^2, dv = e^{-st} dt I do the integration, the uv...

Hello everyone, i have this question and not even sure how to approach it: \frac {di}{dt}+4i+3\int_{0^-}^t{i(z)dz = 12(t-1)u(t-1) and i(0^-) = 0 find i(t) last topics we covered were laplace transforms (and inverse) and dirac delta function. At least some hint to get me started...

Hi everyone, I have this problem and just need someone to check or correct: f(t) = -4e^{-3|t|}(u(t + 3) - u(t-1)) where u(t) is step function: u(t) = 1 for t >= 1 and 0 elsewhere; so, i guess I need to break abs value into 2 cases and have 2 different equations? anyway, here's what I have...

I just want to be sure I understand this correctly, usually L[f(t)] = 1/(s-a), where f(t) = e^{at}, but if it is a complex number would still be 1/(s - complex_number)? techinically, i think it should be, since every number can be reprsented as complex number. Just want to be sure about this...

Hi - I really need someone to show me step by step how to do an Inverse Laplace transform using a contour integral. The one I would like to understand is the frequency function 1/sqrt(s) Thank you if you can help me out. Steve

I am sort of stuck on this one: compute Laplace trasnform of this signal (directly by evaluating the integral) f(t) = cos(pi*t + theta)*delta(t-2); I know what the LT integral looks like, but I don't think I'm evaluating it right. Would the answer be just: cos(pi*t + theta)*e^(-2s) ...

How can I find the inverse Laplace transform of the following function? Y(s) = \frac{1}{s^2 + \frac{1}{s}}

Hi. I'm trying to find the Laplace transform of: sin[3t] ( h[t - pi/2] - h[t] ) I realize that this function is only valid for 0 <= t <= pi/2. Since the limit is not from zero to infinity (0 to pi/2 instead) how can I use the laplace tranform definition to solve this? Also, does...

I am asked to find the inverse laplace transform of the following function: \frac{ \left( s+3 \right) }{ \left( s+1 \right) \left( s+2 \right) } Using tables, can anyone help me understand why the answer is: 2e^{-t} - e^{-2t} I'm completely loss on this one, and yet the book...

I have this laplace transform that I need to solve: y''-6y'+13y=0 y'(0)=2 y(0)=-3 I figured out my Y(s)=(-3s+20)/(s^2-6s+12). All I need to do is take the inverse laplace of this but I can't figure it. I know I need to split it into two fractions, but after that I'm lost. I'd appreciate...

Use the Laplace transform to solve the given initial value problem. y"+[w^(2)]y=cos2t, w^(2) does not equal 4; y(0)=1, y'(0)=0 I tried doing the problem, and I got up to Y(s)=[(s^(3)+5s]/[s^(2)+w^(2)], which hopefully is correct. Now I'm having trouble using the Laplace transforms to...

need help compute the laplace transform of h(t)= -5t^2 I took the integral((-5t^2)e^-(st)) i forgot integration by parts so i did it the hard way in my head and finally got lim t -> oo 5[(-1/s)(t^2)(e^-st) - (2te^-st) - (2se^-st)] 0--oo i got 10s but the book says -10/s^3 did i get the...

I have a proplem to analitic calculate this : (k/p^2)*LaplaceTransform[Sqrt[z^2+2p*z]/(z+p)],z,k]+ (1/p^2)*LaplaceTransform[-Sqrt[z^2+2p*z]/(z+p)^2],z,k] Im(k)=0, k>0 Im(p)=0, p>0 The Mathematica 5 doesn't calculate this. Very glad to help.

I can't seem to integrate this properly and can't find the proper algebraic substituition for it. There's a table of laplace transforms and sin ax is included but I'll really like to do it myself. {\cal L} (sin ax)

Can anyone get me started with the following transforms using convolution theory? L^-1 {1 / (s^2+k^2)^2} and L^-1 {8 / (s^2+1)^3} Any help would be greatly appreciated CA Casanovamp@yahoo.com

Can somebody help me to find the inverse laplace transform of these functions exp(sqrt(1+s)) sqrt(1+s)) I tried solving these using MATLAB and mathematica,it is unable to give a result. Do they contain any closed form solution or should i have to go for a numerical technique to solve...

let S be the Unit Step function for a function with a finite jump at t0 we have: (*) L{F'(t)}=s f(s)-F(0)-[F(t0+0)-F(t0-0)]*exp(-s t0)] so: L{S'(t-k)}=s exp(-s k)/s-0-[1-0]*exp(-s k) = 0 & k>0 but S'(t-k)=deltadirac(t-k) and we know that L{deltadirac(t-k)}=exp(-s k) so...

Hello, Anyone good source on how to do Laplace transforms? My teacher is really really bad and I have a test next week on it. I have no clue on how to do any of them. :cry: Example problems attached. Thanks for any help at all. :smile:

Mathematically, these are three distinct, although related beasts. Laplace transform (function f(x) defined from 0 to inf) integral of f(x)e-xt, defined for t>=0. Fourier transform (function f(x) defined from -inf to inf) integral of f(x)e-itx defined for all real t. Complex Fourier series...

This question may be obvious but I am stumped. I know the definition of a Laplace Transform is integration of e^(-st)f(t). However, I don't know how to integrate with both s and t variables included. If anyone could provide insight I would appreciated it.

Having difficulty finding the inverse laplace transform! Hello everyone, I am really stuck on finding the inverse Laplace transform for this: f(s)=\frac{5se^{-3s} - e^{-3s}}{s^{2}-4s+17} Heres my reasoning: I feel that I should rewrite the denominator in some kind of form such as (s-2)^2...

Hello everyone, well thus far in our introduction to Laplace Transforms I am understanding much of what is being shown, however I am having the unsatisfying task of having to solve the following DiffEQ, y^3-8y=\sum_{k=0}^{3}\delta(2t-k\pi), y(0)=0, y'(0), y"(0)=0 I am having a great...

How would you go about finding the limits of the general laplace transform function for periodic functions?

The well know Laplace Transform, that is : int (e^(st)f(t)) dt 0->00 was really reated by Laplace or other person ? And how he concluded that ?

Hi I am currently working my way through a control systems textbook and I am bringing my understanding of the relevant mathematics up to speed. I have happened across the Laplace Transform which I am happy enough with. I am concerned however that given the fact that this is a real project I may...

Find Laplace Transform of... (e^t + 2t^4 - cos (4t) + 10) Thank you

Ok, using the definition of Laplace transforms to find \L\{f(t)\} Given: f(t)=\{^{\sin{t}, 0\le{t}<{\pi}}_{0, t\ge{\pi}} So, this is what I did: \L\{\sin t\}=\int^{\pi}_{0} e^{-st}\sin t dt+\int^{\infty}_{\pi} e^{-st}(0)dt =\int^{\pi}_{0} e^{-st}\sin t dt...

The closest I've been able to come so far is just italicizing a normal L, but that's lame

[SOLVED] power series expansion for Laplace transform We are to find the Taylor series about 0 of e^t, take the tranform of each term and sum if possible. So I know the expansion of e^t is 1+x/1!+x^2/2!... x^n/n! then taking the tranform, 1/s + (1/1!)(1!/s^2) +(1/2!)(2!/s3)... and so on then...