Inverse laplace transform Definition and 156 Threads

Dear all, This question is close to the post "Laplace transform of a Taylor series expansion" in PhysicsForums.com, dated Jul06-09. This is my problem: Consider the Laplace transform F(s) = 1 / ( s - K(s) ) , where K(s) = -1/2 + i/(2*Pi) * ln[ ( Lambda - (b+i*s) )/( b + i*s...

Homework Statement F(s) = (s + 1)/(s2 + 1)2 Homework Equations The Attempt at a Solution I used partial fractions but I still end up with a term that includes a (s^2 + 1)^2 in the denominator. I'm pretty much lost at this point.

Homework Statement Find the inverse laplace transform of: 1/(s-2)3 + 25/(s+1)(s-2)2 + s/(s-2)2 The attempt at a solution I get (1/2)e2tt2 + (25/7)e-t-(25/7)e2t+(75/7)te2t for the first two, but I'm not even sure where to start for s/(s-2)2. I was thinking it might use...

http://img215.imageshack.us/i/unledc.jpg/ Using the residue method, I found K1 and K2 to be -2 and 4 respectively. However, where do I go from there?

Homework Statement Use the First Shifting Theorem (translation on the s axis) to find f(t). L-1[(2s-1)/(s2(s+1)3] Homework Equations The Attempt at a Solution This is going to take forever.. Can we assume that I am putting the L^-1 all over the place? [(2s-1)/(s^2(s+1)^3)] =...

Homework Statement Well i did all my work but the forum logged me out and when i submitted it I lost it all because it wanted me to login again >_< anyways i need to find the inverse laplace transform of F(s)=[12*s^2 - (28+2*sqrt(3))*s + 26 + 6*sqrt(3)]/[(s-3)(s^2-2s+2)] Homework...

can someone please help me find the inverse laplace transform of the following: http://www.webpagescreenshot.info/img/694286-34201141544am.png i do not know how to solve for this due to the e^-20s shift in the denominator... is there a way to change this function to make it easier to solve?

Hi, all. I am doing an inverse Laplace transform and meeting some difficulty. InverseLaplaceTransform[1/(Sqrt[s]+a)]. Using Mathematica I found the result, however, I failed to prove it. I know it should be like \frac{1}{2\pi i}\int_{\gamma-i\infty}^{\gamma+i\infty} \frac{1}{\sqrt{s}+a}ds...

So my professor is really bad and I've had to try to learn to learn this stuff myself. But I have no idea where to start and where to go. Problem: X(s) = \frac{3(3s+2)}{9s^{2}+12s+4}Attempt All I've been able to figure out so far is: -> X(s) = \frac{3}{(3s+2)^{2}} * \frac{1}{(3s+2)}} But...

Homework Statement Compute Y(t). Homework Equations Y(s)= (s(2s+11)+ω(8s+4ω^2))/((s^2+ω^2)(s+9)(s+2)) The Attempt at a Solution (s(2s+11)+ω(8s+4ω^2 ))/((s^2+ω^2)(s+9)(s+2))= A/(s^2+ω^2 )+B/(s+9)+C/(s+2) Every example I have looked at does not have the ω variable, but I...

Homework Statement Find the inverse Laplace Transform for the function, F(s) = \frac{(3s^{2}+9s+14)e^{-5s}}{s^3 + 4s^2 +7s} Homework Equations The Attempt at a Solution We are given a table of common laplace transforms that we are allowed use to without proof. First I'll...

Hey Guys. Im trying to find an inverse laplace transform for fraction in the laplace domain but can't find it in any of my laplace pair tables. The fraction is: 1/(s + 4)(s + 4)(s + 8) Does anybody have any suggestions?

Homework Statement Find the inverse Laplace Trasnform of, F(s) = \frac{s^{2}}{(s^{2} + 9)^{2}} Homework Equations The Attempt at a Solution We are given a table with a bunch of common Laplace transforms and their inverses but I can't seem to get this one. Can anyone nudge...

Homework Statement Take the Inverse Laplace Transform of: Y(s)=\frac{1}{\tau s+1}\cdot \frac{1}{s} 2. The attempt at a solution I know: L^{-1}(\frac{1}{\tau s+1})=\frac{1}{\tau}e^{\frac{-t}{\tau}} and: L^{-1}({\frac{1}{s}})=1 But how to continue?

Hey everyone. I've got through most of a problem that involves finding an inverse laplace transform, but I am stuck at one part that requires algebraic manipulation. The function is 1/[s(2s2+2s+1)] So far I have modified it too look like .5/[s(s+.5)2 +.52](1/.5) I'm not sure how to...

F(s) = \frac{1}{K^s} where K is a positive real.

Homework Statement \frac{s}{(s-a)(s-b)} Homework Equations Now I know that it results in: [tex]\frac{ae^(at)-be^(bt)}{a-b}[\tex] The Attempt at a Solution OK, I don't have the slightest clue where to begin. Could someone point me in the right direction? I've looked at all...

Homework Statement Find the unit impulse response for the operator D^4 + I, using the Laplace transform. Homework Equations The Attempt at a Solution w^(4) + w = δ(t) s^4W + W = 1 W = 1 / (s^4 +1) Now, I need to find the inverse laplace transform of W. But I don't know how to simplify W...

Homework Statement I need to find the inverse Laplace transform of s/(s^2+a^2), where a is a constant, by the method of residues. I need to prove the part of the contour not actually relating to the desired integral tends to zero as R---> infinity. Homework Equations The...

Homework Statement Calculate the inverse Laplace transform of exp(-as)/s (a is a constant). Homework Equations The Attempt at a Solution I need to calculate the integral (1/2*pi*i)int(c-i(inf), c+i(inf))(exp(s(t-a))/s). I'm guessing I need to integrate around a circular...

Homework Statement ...find the inverse transform of the given function. F(s)= (2s+2)/(s2+4s+5) Homework Equations On another page, I see these 2: f(t)=eatsin(bt)--------->F(s)=b/[(s-a)2+b2) f(t)=eatcos(bt)--------->F(s)=(s-a)/[(s-a)2+b2) The Attempt at a Solution This is my first time...

I am asked to find inverse laplace of (3s+5)/(s^2-6s+25) I do partial frac and get (3s)/((s-3)^2+16) + (5/(s-3)^2+16) I do the translation and get [(3s)/s^2+16 + 5/(s^2+16)]*e^3t My final answer is e^3t[3cos(4t) + 5/4sin(4t)] but the book says the sin term should be 7/2sin(4t)? I say...

Homework Statement Determine the inverse Laplace transform of the given function F(s) = (2s+1) / (s^2 + 16 ) Homework Equations the LaPlace transform of different functions The Attempt at a Solution I divide the above equation into 2 fractions one with the 2s in the numerator...

L^{-1}(\frac{1}{\sqrt{1+s^2}})=?

Homework Statement hi guys, i need to find the inverse Laplace transform of s/((s+1)^(2) +4) the acual question is an IVP, i have worked trough it and am just about finished but i am stuck on this transform. how would you go about getting this into a form that can be transformed like...

According go Wikipedia the inverse Laplace Transform is given by: \mathcal{L}^{-1} \{F(s)\} = f(t) = \frac{1}{2\pi i}\lim_{T\to\infty}\int_{\gamma-iT}^{\gamma+iT}e^{st}F(s)\,ds, How do you probe this? I'm surprised that it doesn't depend on the value of \gama...

My books aren't clear at running through these inverse laplace transforms and this ones got me snookered. I'm trying to perform the laplace transform of: 1/s + 40/(24s^2 + 40s + 40) Factor out 24 becomes 1/s + 1.667/(s^2 +1.667s +1.667) Finding A, B, C A/s + Bs+C/(s^2 +1.667s...

L-1(1/(s+2)3) I don't see this one in the table. How do I solve the inverse Laplace transform? I know from class notes that the answer is (1/2) t2e-2t But I don't know to get it. Thanks!

Hello, I know normally giving solutions is frowned upon, but I have lost my colleagues data sheets and desperately need this transform to continue my work. I am looking for the Inverse Laplace Transform of the Transfer Function: H(s) = 1 / (s^2 + 20s + 5K) where K is an as yet unknown...

I'm having some trouble getting the inverse Laplace to the following problems...I need some help F(s)=24/s^5 F(s)= 4/[((s-2)^2)+25 F(s)= s/(s-1)(s+1)

Homework Statement Find f(t). Homework Equations L^{-1}\left\{\frac{s}{s^{2}+4s+5}\right\} The Attempt at a Solution I tried completing the square to get to the solution and I ended up with: L^{-1}\left\{\frac{s}{s^{2}+4s+5}\right\} =...

Homework Statement This isn't a homework, I'm just trying to recap for a mid-term. Anyways, it's about inverse Laplace transformation and this crap is starting to piss me off! How the heck are you supposed to go from \frac{ \frac{-U}{s}}{R+sL+ \frac{1}{sC}} to - \frac{2 \sqrt{10}}{...

How do I do the inverse of this? 1/(s+a)n is not in the table. \begin{array}{l} Y\left( s \right) = \frac{1}{{\left( {s + 4} \right)^4 }} \\ y\left( t \right) = L^{ - 1} \left[ {Y\left( s \right)} \right] \\ \end{array}

matlab: >> ilaplace(exp(-1*s)/(s+3)^3) ans = 1/2*heaviside(t-1)*(t-1)^2*exp(-3*t+3) But I think there should be an additional exp(3) multiplied by all. =exp(-1*s)/(s+3)^3 =exp(-1*(s+3)+3)/(s+3)^3 Taking out exp(-3t). In above step I did (s+3)+3 because exp(-3t) says all...

Homework Statement Determine the inverse Laplace transform of 1/((s^2 +1)*(s-1)). The answer is 1/2*(e^x - cos(x) - sin(x)). Homework Equations We get a table of known inverse Laplace transforms. The Attempt at a Solution I tried to break this up using partial fractions...

Homework Statement Find the inverse laplace transform of (s+1)/ (s^2 + 4s + 5) + e^-2s / 3s^4 Homework Equations The Attempt at a Solution For the first one (s+1) / (s^2 + 4s + 5), I completed the square for the denominator so (s+1) / [(s+1)^2 + 1] Now it gets...

Homework Statement determine the inverse laplace transform f(t) of the function Homework Equations F(s) = 3/s - (4e^-s)/s^2 + (5e^-2s)/s^2 The Attempt at a Solution i broke it up into the 3 part and got them seperatly which gave me f(t) = 3 - 4u(t-1)(t-1) + 5u(t-2)(t-2)...

My goodness.. I have not come across an inverse Laplace transform like this. My teacher let's us just use a chart to figure them out, but this is definitely not on there. How do I find the inverse Laplace transform of: { (1/2)+[(5e^-6s)/(4s^2)] } / (s+5) I already used partial fractions to...

1. Find v(t) if V(s)=\frac{2s}{(s^{2}+4)^{2}} Ans: v(t)=\frac{1}{2}tsin2tu(t) 2. Homework Equations : V(s)=\frac{a_{n}}{(s-p)^{n}}+\frac{a_{n-1}}{(s-p)^{n-1}}+\cdots+\frac{a_{1}}{(s-p)} a_{n-k}=\frac{1}{k!}\frac{d^{k}}{ds^{k}}[(s-p)^{n}V(s)]_{s=p} 3. Attempt at a solution...

Given... (2s^{2}+1)e^{-s} ------------------ (s - 1)(s^{2} + 4s + 5) Find the inverse Laplace Transform. I am unsure where to start and am just looking for a little direction, not an answer. From past experience, I am assuming I will have to rewrite this in another form...perhaps by...

Hello, I have a fairly straight forward question regarding an inverse laplace transform. The function follows along with the solution. The solution (provided in my text) has been confirmed by Maple; however, i cannot account for the (1/3) in the solution. Any help would be greatly...

Homework Statement Use Laplace Transforms to solve the following initial value problems a. t\,y''\, - \,t\,y'\, + \,y\; = \;2\;\;\;y(0)\;=\;2\;\;\;y'(0)\;=\;-1 b. y''\,+\,2\,y'\,-3\,y\;=\;\delta(t\,-\,1)\,-\,\delta(t\,-\,2)\;\;\;y(0)\;=\;2\;\;\;y'(0)\;=\;-2 Homework Equations Laplace...

I couldn't figure the sol'n for this problem Could somebody help? Thanks a lot Find the following Inverse Laplace transform (L^(-1))*[1/(4s+1)]:frown:

Gents, I have this problem: find the inverse laplace transfor for Y1(s) = exp(-s)/s^2 Y2(s) = {1/[4*(s+1)]}*exp(-2*s) my solution is: using the 2nd shifting theroem y1(t) = (t-1) H(t-1) y2(t) = (1/4)*exp(2-t)*H(t-2) Is my solution correct?

I am trying to find the inverse LaPlace transform of F(s)=\frac{2s+12}{s^2+6s+2\sqrt{2}} Using partial fraction decomposition on the above rational expression seems tedious. Is there any other method? Thanks

My book on signal processing says that: f(t) = \frac{1}{2\pi j} \int_{c-j\infty}^{c+j\infty} F(s) e^{st} ds = \lim_{\Delta s \to 0} \sum_{n = -\infty}^{\infty} \Big[ \frac{F(n\Delta s)\Delta s}{2\pi j} \Big] e^{n\Delta s t} I don't get this. How/Why can you write a integration over a...

Homework Statement 1/s^5 Homework Equations I was thinking I need to use n!/s^n+1 The Attempt at a Solution But n would then be 4, so n! will be 24. Not sure what to do?

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

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...

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...