Laplace transforms Definition and 177 Threads

Hi, Is the final value theorem an appropriate way to deduce if a specific differential equations converges or diverges?

Homework Statement Find the inverse laplace transform. (see figure attached for question as well as my attempt) Homework Equations The Attempt at a Solution I came up with a different answer than the given solution, and I can't figure out where I went wrong. We are given a...

Homework Statement Find the Inverse Laplace Transform of \frac{200}{s^{2}+10s+200} Homework Equations The Attempt at a Solution Normaly use partial fractions to get simple functions that can be transformed using a table of transforms.

Y' + 8y = e^-2t*sint, with initial condition y(0) = 0 Alright so I've been working on this one for about an hour, I really don't know why but I'm having major problems with these types of problems, whether i don't understand how to set it up or I don't understand partial fraction...

Homework Statement Consider the initial value problem y'' + 1/3y' + 4y = fk(t) with y(0) = y'(0) = 0, fk(t) = 1/2k for 4 - k < t < 4 + k 0 otherwise and 0 < k < 4. (a) Write fk(t) in terms of...

Working through a recent assignment, I've been dealing with an inverse laplace transform \mathcal{L}^{-1}\left[\frac{e^{-kds/v}}{(s+1)^2}\right] that Maple can't solve, yet I can do this by hand and WolframAlpha will solve it too. Should Maple be able to solve this (perhaps it requires extra...

Laplace Transforms Help! Homework Statement X' + 7X = 5cos2t I.C. x(0)=0 x'(0)=0

Homework Statement http://img231.imageshack.us/img231/3904/q2a.png The Attempt at a Solution Below is a screenshot of my Maple worksheet. I am currently stuck on part (a). I have taken the Laplace transform of both sides of the equation, solved for Z(s), then converted it Heaviside form, yet...

Homework Statement Doing some Laplace transform stuffs and I've got Y(s) = \frac{1}{(s+1)(s^{2}+2s+2)} Using the normal method 1 = A((s+1)^{2}+1) + B(s+1) I'm not sure this method is valid though as we had a complicated term (s+1)² + 1 after A. I can find A to be 1, but I don't trust my...

Solve the following given y(0) = 0 & y'(0)=1: y′′+3y′+2y = u2(t), such that u2(t) is a heaviside step function Here's what I've got so far, =>s2Y(s)−sy(0)−y′(0) + 3sY(s)−3y(0) + 2Y(s)= exp(−2s)/s Y(s) = (exp(−2s) + s) / (s(s2+3s+2)) Y(s) = exp(−2s)/(s(s2+3s+2))* + 1/(s2+3s+2)** The...

I'm trying to solve the homogeneous heat equation of a semi-infinite cylinder in cylindrical coordinates for a semi-infinite cable (no theta dependence): \frac{\partial U}{\partial t}=D\left(\frac{\partial^{2} U}{\partial r^{2}}+\frac{1}{r}\frac{\partial U}{\partial r}+\frac{\partial^{2}...

Hi, I was wondering what the prerequisites are for doing Laplace Transforms. I'm just a little confused with one of the examples : \int_0^{\infty} = e^{-sx} dx = [e^{-sx}/s]_0^{\infty} = 1/s I understand that e^{-s(0)} is 1. But where does the e^{-s(\infty)} part go? Is there something I...

Homework Statement Okay, I'm pretty lost in my differential equations class and I'm not sure how to transform the functions Homework Equations f(t)= 1 / (s+2)^2 f(t)= 1 / (s+3)^3 f(t)= 1 / (s^2-3^2) They seem pretty simple, but i have no clue if whether I'm suppose to use 2 formulas or...

Homework Statement Find the Laplace transform of each of the following functions: ... 2. f(t)=eatcos(bt) 3. f(t)=tn, were n is a positive integer Homework Equations As you well know, taking the Laplace of f(t) means ∫f(t)e-stdt from 0 to ∞ The Attempt at a Solution...

Homework Statement I have a couple of problems that I am stuck on. The following: y'' - 6y' + 9y = t y(0) = 0 y'(0) = 1 and y'' - 6y' + 13y = 0 y(0) = 0 y'(0) = -3 Homework Equations y'' = s2Y(s) - sf(0) - f'(0) y' = sY(s) - f(0) y = Y(s) The Attempt at a Solution...

I'm deriving the heat equation using Laplace transforms. I'm up to u(bar) = Aesqrt(s)x + Be-sqrt(s)x. My boundary conditions are lim(x tends to 0) = 0 & this makes A = 0, so u(bar) = Be-sqrt(s)x My other BC is ux(0,t) = -Q My question is how do I get B using this BC? I tried using the def...

Homework Statement L{tcos(t)} Homework Equations Using the laplace transform find the equation. The Attempt at a Solution I already have a really long answer. . .I was just wondering if someone can explain this: Another method (appart from using integration by parts...

Homework Statement Solve the system of first order differential equations using Laplace Transforms: dx/dt = x - 4y dy/dt = x + y, subject to the initial conditions x(0)=3 and y(0)=-4. Homework Equations So far I've used the limited knowledge of Laplace Transforms for first order...

Homework Statement y'' + ty' - y = 0 plugging in the known Laplace formuals i get this... [s^2Y(s) - sy(0) - y'(0)] + [-sY'(s) - Y(s)] - Y(s) = 0 Homework Equations y(0) = 0 y'(0) = 3 The Attempt at a Solution simplying to a linear first order DE -sY'(s) + (s^2-2)Y(s) = 3...

Homework Statement Simply find L{Sin(bt)}Homework Equations My Professor gave us a hint "Use Integration by Parts TWICE" The Attempt at a Solution so i start with the usual limit as N -> infinity the integral of e^(-st)sin(bt)dt Integrating by parts i get ( u = sin(bt) du = bcos(bt) dv =...

Hey guys! I just have a question regarding some notes I've been looking at and trying to understand... Homework Statement Taking the transform: Just wondering, can someone explain to me why the e-3s/s is positive, and not negative because it is originally -u3(t)... Another quick...

Hi, I've been doing Laplace transforms lately...the sums are pretty simple (as much as there is in our syllabus),and I've been practising hard...but the problem is, I don't really understand what I'm doing or why what I am dong is justified at all... I want to know certain things like...

I was looking through some tables of Laplace Transforms on f(t) the other day, and I noticed that in all cases, as s \to \infty, F(s) \to 0. A question that I have been trying to prove is that if \lim_{s\to\infty}F(s) = 0, then does that necessitate whether F(s) can undergo an inverse Laplace...

Homework Statement F(s)=(−2s−2)/((s−1)2+9) Find f(x) by computing L-1[F(s)] = f(x). Homework Equations The Attempt at a Solution I made put (s-1) in place of s in the numerator, then compensated for that by subtracting 2: F(s) = (-2(s-1) - 2 -2 ) / ((s-1)2 + 9) Then s-1...

My teacher said that the computer uses laplace transforms to do integrals , does anyone know how this is done , or where i could find info on this

Can anyone explain the region of convergence to me in english? I understand the Laplace transform and can do it with my eyes closed, but I can't figure out how to figure out the ROC. I've scoured the internet, and every definition is vague or just incomprehensible by me. Thanks!

According to wikipedia the greens function is defined as: L G(x,s) = - \delta(x-s)\, http://en.wikipedia.org/wiki/Green%27s_function#Definition_and_uses when L is a differential equation then the greens function is the impulse response of the differential equation. If a Hilbert space...

Hi everyone, I'm a long time lurker, first time poster and I was wondering if anyone could help me out with a little Laplace trouble i was having, I am interested in solving the ODE y' = -y+2*y*u(t-1) where u is the heaviside function, Any hints?

can equations involving laplace transforms be converted to Fourier transforms?

the question goes like this: the first part asks to utilize simulink to obtain the graph pattern: the second part requires us to make use of laplace transform and inverse laplace transform to solve the initial value problem: the third part asks us to compare both the results...

Homework Statement Use partial fraction decomposition to find the inverse Laplace Transform. F(s)= 1/[(s+1)(s^2 + 1)] Homework Equations The Attempt at a Solution 1/[(s+1)(s^2 + 1)] = A/(s+1) + (Bs + C)/(s^2 + 1) 1 = A(s^2 + 1) + (Bs + C)(s+1) I do not know how to solve...

Hi all. Lets solve the following ODE by using Laplace transforms y'' - y' = \exp(-x), where y depends on x. Laplace-transforming we obtain (where Y denotes the Laplace-transformed of y) s^2Y(s)-sy(0)-y'(0) - sY(0) - y(0) = \ldots My question is, why we are allowed to do this? Because...

Im trying to find the laplace transform of t^1 x e^(3t) but looking it at the table, it looks like there's two different possible solutions for it. one is for t^(n) x f(t) and the other is for e^(at) x f(t) which one do i choose?

Greetings all/any: Homework Statement Take the Laplace transform of the following initial value problem and solve for Y(s) = L{y(t)} y'' - 3y' -28y = 1 if 0<t<1 0 if 1<t initial conditions: y'(0) = y(0) = 0 a. Y(s) = ? b. now find the inverse transform to...

Homework Statement y'' + 2y' + 2y = t^2 + 4t y(0) = 0 y'(0) = -1 Homework Equations L(y) = Y L(y') = sY - y(0) L(y'') = s^2 Y - s y(0) - y'(0) L(t^n) = \frac {n!}{s^{n+1}} L(a*b) = AB a*b = L^{-1}(AB) The Attempt at a Solution Take the Laplace transform of both sides...

Homework Statement Use the Laplace transform to solve the given initial-value problem. y'' + 9y = cos(3t), y(0)=2, y'(0)=5 Homework Equations L\left\{y''\right\} = s^{2}Y(s)-sy(0)-y'(0) L\left\{y\right\} = Y(s) L\left\{cos(kt)\right\} = \frac{s^{2}}{s^{2} + k^{2}}, s>0...

Homework Statement Find the Laplace Transform of: f(t) = {t, 0<t<1 2, 1<t<2 t^2, 2<=t<=3 } For the first case (t), I get 1/(s^2) for the eqn. t^n = n!/s^(n+1) For the second...

Ok, I have two question that have me stuck. I understand heavyside functions and how to do a laplace transform on them but, they've thrown me a curve ball. I'm sure I'm just making it more complicated then it needs to be. Here is problem number one. g(t) = 2t for 0 <= t < 1...

Little homework problem that I'm beating myself up over... Solve: xy'' - 2y' + xy = -2\cos x Using the method of Laplace transforms... So I do some jiggling and get to: (1+s^{2})\frac{dF}{ds}+4sF(s) = \frac{2s}{s^{2} + 1} To which I find the following solution: F(s) =...

Homework Statement solve the ivp using laplace tranforms y''+2y'+2y=0 y(0)=1 y'(0)=-3 Homework Equations The Attempt at a Solution get to Y(s)[s^2+2s+2]=s-1 Y=(s-1)/[s^2+2s+2] ^^^ don't know how to simplify the denominator to solve using Laplace transforms. If I had...

Homework Statement I have three inverse laplace transforms I can't solve, they are, i) (s-1)/(s^2 + 8s + 17) ii) (s+3)/(s^2 + 4s) iii) 2/[(s+1)*(s^2 + 1)]Homework Equations The laplace transform table...

Homework Statement The problem is this: y'' - 4y = e^{-t} , y(0) = 1, y'(0) = 0 Homework Equations L{y(t)} = Y(s) L{y'(t)} = sY(s) - y(0) L{y''(t)} = s^2Y(s) - sy(0) - y(0) The Attempt at a Solution Ok, so I plugged the Laplace transforms for y'' and y into the equation as...

Homework Statement L[f(t)]= 1/(s^2+1)^2 + 1/(s^2+1) L[f(t)]= ln(s+a) where 'a' is a constantHomework Equations The Attempt at a Solution I know that the inverse laplace of 1/(s^2+1) is sin(t), but how do I deal with the squared form of it. I have never encountered a logarithmic funcion for...

Homework Statement y'' + y = delta(t-2*pi) The Attempt at a Solution I have solved this using laplace transforms. Y = e^(-2*pi*s)/(s^2 + 1) + 10s/(s^2 + 1) so that y = sint*u(t - 2*pi) + 10 *cost what I don't understand is this function is not definied for t<0. According to...

Using Laplace transforms, find the solution of Abel's integral equation: \int^{x}_{0}\frac{f(u)}{\sqrt{x-u}}du = 1 + x + x^2 I recognized that the integral is a Laplace convolution, leading to: (f*g)(x) = 1+x+x^2 where g(x)=x^{-1/2} So: L(f*g)=L(1)+L(x)+L(x^2)...

Hi all, 2 questions here 1) I've been doing some questions on laplace transforms and have been running into some trouble getting my answers into the same form as the answers given with the questions. For example: f(t) = 1 - e^(-t) Using the linearity property i got 1/s - 1/(s-1) which is...

Hey can anyone tell me the method to solve this, I can do inverse linear eqns and such but i don't know how to solve this type of question: Use Laplace transforms to solve the following systems of linear equations (a)dx/dt= 3x(t) − 4y(t), dy/dt= 2x(t) + 3y(t), with initial conditions...

Hi hows it going, Im currently doing a linear maths course, i suppose it'd be introductory. I am using Elementary Linear algebra by Howard anton and find that very good. However the course goes on to deal with laplace transforms and Fourier series, can anyone recommend a good (introductory)...

1. Please see attachment for Question I've put it into microsoft eqn editor. 2. I have not got a clue where to begin i don't want anyone to do it for me but some information on how i can do it for myself would be appreciated. 3. as above

Is it possible to use a laplace transform to solve a problem like x' + x = T where x is a function of T and x(0) = 5 and x(4) = 7 Or can you only solve initial value problems?