Inverse laplace transform Definition and 165 Threads

I can't seem to part of an inverse Laplace transform correct. \begin{align*} f(t) &= \frac{6}{5}\mathcal{L}^{-1}\bigg\{\frac{1}{s + 2}\bigg\} + \frac{3}{5}\mathcal{L}^{-1}\bigg\{\frac{3s - 1}...

Homework Statement ##\mathcal{L}^{-1}\Big\{\frac{s}{(s^2+1)^2}\Big\}## I'm trying to figure out how to find the inverse Laplace transform of this expression. Is this something you just look up in a table or is there a way to find it directly, maybe by Convolution?

Please refer to the attachment. For part a) so far I have: $e^x = 1 + \frac{x}{1!} + ...+ \frac{x^n}{n!}$ So $S^\frac{-1}{2}e^\frac{-1}{S} = S^\frac{-1}{2}(1 -\frac{1}{S} + \frac{1}{2!S^2} - \frac{1}{3!S^3} + \frac{1}{4!S^4} + ... - ...)$ I don't think my $S^\frac{-1}{2}$ on the outside is...

Homework Statement I'm stuck trying to find out the inverse Laplace of F(s) to get y(t) (the solution for the differential equation): Y(s) = 1 / [ (s-1)^2 + 1 ]^2 The Attempt at a Solution I tried using a translation theorem and then apply the sine formula, but the denominator...

I am reviewing some material on Laplace Transforms, specifically in the context of solving PDEs, and have a question. Suppose I have an Inverse Laplace Transform of the form u(s,t)=e^((as^2+bs)t) where a,b<0. How can I invert this with respect to s, giving a function u(x,t)? Would the inverse...

Homework Statement Find the inverse Laplace transform of e^(-3pi*s)/(s^2+2s+3). Homework Equations I know that you're supposed to factor out the e^(-3pi*s) and the other part becomes 1/(s+1)^2+2 but how do you get the answer? I'm confused. The Attempt at a Solution The answer is...

Homework Statement Find the Inverse Laplace Transform of \frac{1}{(s^{2} + 1)^{2}} Homework Equations The Attempt at a Solution I tried using partial fractions but it didn't work. It looks like a cosine transform, but I don't know what else to do. Help please :(

Homework Statement Find the inverse Laplace transform of F(s)=(8s^2-4s+12)/(s(s^2+4)). Homework Equations A/s+(Bs+C)/(s^2+4) 8s^2-4s+12=A(s^2+4)+(Bs+C)(s)=As^2+4A+Bs^2+Cs=s^2(A+B)+Cs+4A 8=A+B C=-4 A=3 B=5 L^-1 (3/s)+L^-1 ((5s-4)/(s^2+4)) =3+ (Now I'm stucked.) The Attempt...

Homework Statement Find the inverse Laplace transform of F(s)=(2s-3)/(s^2-4). Homework Equations I don't want to find the answer by looking at the Table. F(s)=2s/(s^2-4)-3/(s^2-4) The Attempt at a Solution The answer is f(t)=2 cosh 2t - (3/2) sinh 2t.

Having difficulty with L-1 {1/(s^2+s-20)}: Should I make it L-1 {1/(s+5)(s-4)}? I'm stuck.

what is the inverse laplace transform of (2s)(1/(s-2))? could i use the identity ∫f(T)g(t-T)dT=F(s)G(s)? i was hesitant so i figured i'd just ask before i continue..

Homework Statement L-1{\frac{s}{s^2+4s+5}} Homework Equations \frac{s-a}{(s-a)^2+k^2} \frac{k}{(s-a)^2+k^2} The Attempt at a Solution I completed the square for the denominator and got: L-1{\frac{s}{(s+2)^2+1}} (a= -2, k=1) But how do I get rid of the s in the numerator? Or do I have...

Homework Statement find the inverse laplace transformation of \frac{5s+4}{s^2} e^{-2s} Homework EquationsThe Attempt at a Solution I have tried to partial fractions \frac{5s+4}{s^2} and I got \frac{5}{s}+\frac{4}{s^2} and I know that the answer must have u(t-2) because of second shifting (...

Homework Statement What is the inverse laplace transform of (1/(s+s^3))? Homework Equations The Attempt at a Solution I looked it up on wolframalpha and got 1-cos(t), but I don't understand how they got that answer. I looked up a basic laplace transform chart and didn't see anything...

Homework Statement Find inverse Laplace transform \mathcal {L}^{-1}[\frac{1}{(s^2+a^2)^2}]Homework Equations The Attempt at a Solution I try with theorem \mathcal{L}[f(t)*g(t)]=F(s)G(s) So this is some multiple of \mathcal{L}[\sin at*\sin at] So \mathcal {L}^{-1}[\frac{1}{(s^2+a^2)^2}]=\propto...

Homework Statement Find the inverse laplace transform of (2/(s+2)^4) using the given table of identities: Homework Equations Here are the given identities: The Attempt at a Solution Alright, I realize that there is a simple identity that I can use with a factorial symbol, but this...

This is a conceptual question on the region of convergence (ROC) and the inverse Laplace transform (ILT). Here the bilateral laplace transform (LT) and the ILT are given by F(s)=L\{f(t)\}=\int_{-\infty}^{+\infty} f(t) e^{-st} dt and f(t)=L^{-1}\{F(s)\}=\frac{1}{i...

I want to perform the inverse of \frac s { [(s+α)^2-β^2](s^2+ω^2)} I know the conventional way is \frac s { [(s+α)^2-β^2](s^2+ω^2)}= \frac{As+B}{[(s+α)^2-β^2]}+\frac{Ds+E}{(s^2+ω^2)} s= (As+B)(s^2+ω^2)+(Ds+E)[(s+α)^2-β^2] \Rightarrow\; A+D=0,\; B+E+2\alpha...

maple issue -- inverse laplace transform equation from a basic series RLC circuit Pretty simple for some of you I know, but I have a laplace transform equation from a basic series RLC circuit ((sV-v(0))/L+si(0))/(s^2+sR/L+1/LC) = I(s) I want to take the inverse laplace of it, I am given all...

Hi guys :) I'm looking to get a jump start on my uni course and have been going through some topics on my own before classes start in the Fall, I've reached the point of Laplace Transform and Fourier maths - and it's tough! I have a small question on an inverse laplace transform equation in...

Hello again. First off, I wasn't sure how to say this in the title but I'm not taking the inverse Laplace transform of a unit step function. I'm taking the Laplace transform of something that comes out to the unit step function. I have this question, which is a similar version of the...

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Homework Statement Hi all, I'm struggling to find the Inverse Laplace transform of the following function: F(s) = (1+ 4e(-s) - 5e(-3s)) / s(s2 + 11s + 55), where F(s) is a Laplace transform Solution should be in terms of complex exponentials and unit step functions. Homework EquationsThe...

Hi all, I'm struggling to find the inverse Laplace transform of the following function: F(s) = (1+ 4exp(-s) - 5exp(-3s)) / s(s^2 + 11s + 55)Any help is appreciated. Thanks

Hi, I recently posted another question about a Laplace transform and now have a question about taking the inverse Laplace transform. Again, my professor did not cover this topic as well as I could have hoped for, and so I am stuck on this problem as well. Again, I understand the idea of Laplace...

I'm attempting to find the inverse laplace transform of \frac{25}{(1-s)^2*(4+s^2)} I get to this point but can't get the values of A B and C when equating coefficients. 25/(s-1)=A(4+s^2)+(Bs+C)(s-1) Also for a separate question: (s+1)/(5-4s+s^2) How do you find the inverse...

Homework Statement Having found the laplace transform of a differential equation. I must now find X(t). All of my work is attached. The problem I am having is fitting my function of s to my table of transforms. I tried using partial fractions but it took me in a loop.The Attempt at a Solution...

Homework Statement Find the inverse laplace transform of \frac{3s + 7}{s^{2} - 2s + 10}Homework Equations completing the square. e^{at}sin(bt) = \frac{b}{(s-a)^{2} + b^{2}} e^{at}cos(bt) = \frac{s-a}{(s-a)^{2} + b^{2}} The Attempt at a Solution F(s)= \frac{3s + 7}{s^{2} - 2s + 10} F(s) =...

Using the laplace transform, find the solution to the differential equation: y'' + y' + y = 0 , y(0)=0, y'(0)=1 Using the laplace transform and its properties I end up with: f(s) = 1/(s2+s+1) How can I find the inverse of this/ does anyone know the inverse of it? Setting y=eax I got a...

Find the inverse Laplace transform of $\displaystyle \frac{2s+7-e^{-2s}}{(s+1)^2}$.

Hi all I have been working on some unique solutions to advection-diffusion type problems. One inverse Laplace transform that I seem to continue to encounter is the following: Inverse Laplace[F(s)] where F(s)=[(1/(((s-α)^2)+β)*exp(-x*sqrt(s/D))] In their classic 1959 text, Carslaw...

IVP Laplace Transform Problem -- Tricky Inverse Laplace Transform Homework Statement Solve x"+x'+x=1, given x(0)=x'(0)=0 Homework Equations The Attempt at a Solution Plugged in transforms: s2*Y(s)-s*y(0)-y'(0)+s*Y(s)-y(0)+Y(s)=1/s Plugged in initial value points, simplified...

Homework Statement Hello all, Having difficulty with this one question that involves complex roots. Here it is: F(s)=\frac{s+3}{s^3+3s^2+6s+4} I tried two different ways to tackle it. First method I divided it right away: F(s)=\frac{s+3}{s^3+3s^2+6s+4}\rightarrow{s^2+6-\frac{14}{s+3}} Is there...

Homework Statement L^{-1}\{\frac{1}{(s^2+4)^2}\} Homework Equations The Attempt at a Solution I have no idea how to solve this. Any idea to being solving the problem would be appreciated.

The link below shows a circuit and the s-domain equation for I1(s) that I have derived; My question is on the portion of the equation containing the "(s+a)" terms. I am trying to arrive at the time-domain equation for I1(s) but instead of arriving at the Laplace transform pair shown in the...

Homework Statement Compute the inverse Laplace transform of Homework Equations http://img267.imageshack.us/img267/696/66451772.png The Attempt at a Solution I tried using partial fraction but no luck.

f(t)=\int^{c+i\infty}_{c-i\infty}F(s)e^{st}ds Why we suppose that all singularities are left from line Re(s)=c?

Homework Statement I'm attempting to find the inverse laplace transform of (5/((2x+3)(4+x^2))) The Attempt at a Solution Here's the solution: http://www.wolframalpha.com/input/?i=inverse+laplace+transform+%285%2F%28%282x%2B3%29%284%2Bx%5E2%29%29%29 There's 3 terms in the solution and 2 are...

Hello everyone, I'm currently enrolled in Control Theory at my University, and part of the coursework requires differential equations; which wouldn't be a problem, if not for the fact it's been 2 years since I've taken D.E. Anyway, over the course of the problem I ran into this little function...

Hello everyone, I'm currently enrolled in Control Theory at my University, and part of the coursework requires differential equations; which wouldn't be a problem, if not for the fact it's been 2 years since I've taken D.E. Anyway, over the course of the problem I ran into this little function...

Homework Statement F(s) = 3/(s(s^2 +2s + 5)) Homework Equations The Attempt at a Solution I have used partial fraction using coefficients. F(s) = (3/5)s - (3/5) ((s+2)/(s^2 +2s + 5)) and reduce s^2 +2s +5 by completing the square F(s) = (3/5)s - (3/5) ((s+2)/((s+1)^2 + 4))...

Homework Statement the questions asks to determine inverse laplace transform of s/(s+4)^4 Homework Equations The Attempt at a Solution this can supposedly be done just using laplace transform tables so I am guessing i need to simplify that to something that's workable but i...

Homework Statement Derive an equation to represent the current flowing in an RLC circuit where R=12 L=1.2 C=30microfrards with an impulse voltage input. Assume zero conditions when the switch is closed. Homework Equations The Attempt at a Solution I have used the voltage to equal...

According to the Wikipedia page, the inverse Laplace transform is f(x) = \frac{1}{2 \pi i} \lim_{y\rightarrow \infty} \int_{x_0-iy}^{x_0+iy} F(s')e^{s'x}ds' Something seems wrong though. If I were to take the Laplace transform this equation, I should get F(s) coming out of the right hand side...

Homework Statement Find the Inverse Laplace Transform of \frac{1}{s}*\frac{\sqrt{s}-1}{\sqrt{s}+1} The Attempt at a Solution for this question i found the singularities to be at 0 and when s = 1. (as the sqrt of 1 is ± 1) there is also a branch point that runs from 0→-∞. so if you...

Homework Statement Find the inverse Laplace Transform of \frac{1}{s}\frac{\sqrt{s}-1}{\sqrt{s}+1} Homework Equations The complex inversion formula (well known) The Attempt at a Solution The first thing is finding singularities and branch points and so on. From the \frac{1}{s}...

Good day to all, I encounter this expression in analyzing my equation after transform it using Laplace Transform, to get the answer I have to invert it back, I have no idea on how to find its inversion. [text]-\text{Cosh}\left[\sqrt{2 s+s^2} x_0\right]+\text{Cosh}\left[s h_0+\sqrt{2 s+s^2}...

Find the inverse Laplace transform $F(s)=\frac{4}{s^4+4}$ I tried factoring out the solution, but run into the problem with the imaginary numbers and am still stuck with the s^2+2j, which I have to factor out once more, and that's where the problem gets even messier. What do I do?

Homework Statement Find the inverse Laplace transform of the following function 1/[s(s2 + 4)2] Homework Equations 1/ (s2 + \omega2)2 = (1/ 2\omega3) (sin\omegat -\omegat cos\omegat) The Attempt at a Solution L-1 = (1/s) (1/ s2 +22)2 = (1/16) (sin 2t - 2t cos 2t) as the Laplace...

Homework Statement Find the inverse laplace transform: {\cal L}^{-1}\{e^{-\sqrt{s-a}c}\} where a and c are constants. s is the complex variable.Homework Equations Bromwich integral: \frac{1}{2\pi{}i}\lim_{T\rightarrow \infty}\int_{\gamma-Ti}^ {\gamma+Ti}e^{st-\sqrt{s-a}c}ds...