Laplace transform Definition and 752 Threads

Can someone help me out with the proof of the Laplace transform of the function tn? I did have a go at this one. L[t^n] = \int_0^{\infty} t^n e^{-st}dt = t^n\frac{-e^{-st}}{s}\vert_0^{\infty} + {1\over s}\int_0^{\infty} nt^{n-1}e^{-st}dt ={n\over s}\int_0^{\infty} t^{n-1}e^{-st}dt ={n\over...

How do i find the inverse laplace transform of s/(s-2)^2

I have to find the laplace transform of (t+2)sinh2t my answer is (4s/(s^2 + 4)^2 ) + (4/(s^2 - 4)) is this simplified as much as possible...?

My understanding of the laplace trasnform isn't so great so i would appreciate some help with this question please: find the laplace transform of (t+2)sinh2t now i know the laplace transform of sinh2t is 2/(s^2 -4) as this is a standard rule... looking through textbooks they show the...

http://xs104.xs.to/xs104/06322/ssss.gif Hello all ^^ What is the difference between the two definitions thanks a lot

I wish someone would help me to verify my answer and working. I don't have the answer for the question. :frown: http://www.mrnerdy.com/forum_img/laplace.jpg Is there a better working method?

Okay, I know this is alot... but I am stuck, so here goes... Use the method of Laplace transform to solve the initial value problem y''+3ty'-6y=0, y(0) = 1, y'(0) = 0 L\{y'' + 3ty' - 6y\} = L\{0\} s^{2}Y(s) - sy(0) - y'(0) + 3L\{ty'\} - 6Y(s) = 0 s^{2}Y(s) - s(1) - 0 -...

Hi, I need to find the piece wise function whose the the Laplace Transform is: 2/s+e-3x(1/s2)+4e-3x(1/s) I found for f as function of the unit step function u: f(x)=2+x*u(x-3)+u(x-3) Now I have difficulty to put the function in piece wise form like: f(x)= 2 for 0<x<2 and f(x)=...

First off, I hope these images show up - I don't have time to figure out this latex stuff atm, so it's easier just to throw the formulae together in openoffice. I'm working on the Laplace Transform for http://home.directus.net/jrc748/f.gif Which is obviously...

I have to find the laplace transform of cos(at) * cos(bt) and express it as a ratio of two polynomials. I converted both of the cosines into exponentials, and took the laplace transform of those. I think I'm getting confused on the complex side of things. I get a few things like...

Our professor asked us to derive an expression for the laplace transfrom of t^n. I did a few examples in MatLab and gathered that the Laplace Transform of t^n = n!/s^(n+1). I'm pretty sure this is correct, but I don't think my professor will be happy with it. I don't really know how I should...

how do i find the laplace transform of the following error function without using tables? f(t)=erf(t^(1/2)) i've been trying really long but i seem to be stuck in a loop of erf

i have f(t) defined piece-wise and continous.. f(t) = 0, t < 2pi t-pi , pi <=t<2pi 0 , t >=2pi i have so far g(t)=U_pi*f(t-pi)-U_2pi*f(t-pi) if i do the laplace, i get e^-pis/s^2-e^-2pis/s^2 in the book, they have e^-pi*s/s^2 -e^-2pi*s/s^2 (1+pi*s) I am not...

I need to show that for f(t)=f(t+T) on [0,infty), that the Laplace Transform is: \mathcal{L}\left[f(t)\right]=\frac{\int_0^Te^{-st}f(t)\,dt}{1-e^{-sT}}. The first thing I did was to write the transform as...

In the HW section, the following equation was proposed: ty(t)=\int_0^t \tau^{1-\alpha}y(t-\tau)d\tau;\quad \int_0^\infty y(x)dx=1 Link to HW thread: https://www.physicsforums.com/showthread.php?t=97562 Using Laplace Transforms: Y(p)=\mathcal{L}\left\{y(t)\right\} and noting the...

I have the problem, ty(t)= \int_{0}^{t}\tau^{\alpha-1}y(t-\tau)d\tau subject to the constraint that \int_{0}^{\infty}y(t)dt=1. In need to get the answer in the form of, Y(p)=something (where Y(p) is the Laplace transform of y(t)). I can see that the right hand side is...

Question about the maclaurin serie and the laplace transform. For maclaurin serie i wonder, the function used for teh maclaurin development must be derivativable to infinity? What is the difference between the fouri transform and the laplace transform? As i understood it, it's just the...

how do i find the laplace transform of log[x]

What is the laplace transform of http://img150.imageshack.us/img150/8145/laplacetransform6wk.jpg

I have y"+y=t , y(0)=1, y'=0 After Laplace transformation a got: (S^3+1)/(S^2(S^2+1)) After I made a partial fraction expansion (S^3+1)/(S^2(S^2+1))=a1/S^2+a2/S+a3/(S^2+1) (1) It comes to a system where a2=1 a1+a3=0 (2) a2=0 a1=1 Here I am getting confused...

Ok... I'm working on this laplace transform, and I'm getting stuck on the partial fractions part on this one problem. If someone could help me out with setting it up, I would be very appreciative. \frac{s}{(s^2+4)(s^2+\omega^2 ) } After trying to set it up, I get something like...

Hi How would I find the inverse laplace transform of this? I(s) = \left( \frac{1}{s(1+e^{-s})}\right) \left( \frac{1}{Ls+R}\right) i(t)=? L, R are constants. I recognize the first term to be a geometric progression (square-wave function). With an infinite number of terms in that...

there are two loops in an electrical circuit. I've got two equations and two unknowns. here are the equations v(t) = I1*R1 + 1/c*int(I1*dt) - 1/c*int(I2*dt) - first loop 0 = LdI2/dt + R2*I2 - 1/c*int(I1*dt) + 1/c*int(I2*dt) - second loop the capacitor is in the branch between the two...

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...