Laplace transform Definition and 752 Threads

##\mathcal{L}\{f(t)\}=F(s)## \mathcal{L}\{e^{at}\}=\frac{1}{s-a},Re(s)>a \mathcal{L}\{\sin (at)\}=\frac{a}{s^2+a^2}, \quad Re(s)>0 \mathcal{L}\{\cos (at)\}=\frac{s}{s^2+a^2},Re(s)>0 If we look at Euler identity ##e^{ix}=\cos x+i\sin x##, how to get difference converge intervals...

\mathcal{L}\{f(t)*g(t)\}=F(s)G(s) Is there some relation between F(s)*G(s) and f(t)g(t)? ##*## is convolution.

Homework Statement Laplace Transform teat Homework Equations The Attempt at a Solution http://img521.imageshack.us/img521/6449/homeworkhelp.jpg Not sure where I am going wrong. I feel like I did integration by parts incorrectly, because the anser I have boxed is not the...

Homework Statement f(t) is a piecewise function: {0 0<= t< 1 {t*exp(2t) t = >1Homework Equations F(s)= L{f(t)}The Attempt at a Solution F(s)= L{t*exp(2t)} for this problem I just took the Laplace Transformer directly from the table which is: n!/ (s-a)^(n+1) and after plucking in the...

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...

Homework Statement Find f(t) for: 2\int_{0}^{t}f'(u)sin(9(t-u)du +5cos(9t), t\geq0 The Attempt at a Solution F(s)=2\frac{9(sF(s)-f(0))}{s^2+81}+\frac{5s}{s^2+81} At this point i don't know what to do with f(0) since there are no initial conditions. What do I do with it?

now say we have cos^2(3t), how would you go about computing it with the 3t? i can manage cos^2(t) but I'm not sure how to take it that one step further in the link below is what I've managed so far.. [SIZE="5"]SOLVEDI worked it out. If anyone's interested in the future, Just start it off as...

I am trying to do laplace transform of y(t)=e^{-at}\cos (bt)\;. The answer should be: \frac {s+a}{(s+a)^2+b^2} But here is my work, I can't get rid of the -ve sign. I must be too blind to see the obvious, please help: \overline{y(s)}=\int^∞_0 e^{-(s+a)t}\cos (bt) dt\;=\; \frac 1 b...

Homework Statement d'^2 (y)/dt + 4 (dy/dt) + 4y = -7(e^(-3t)). Here I need to forced response of this differential equation using laplace transform technique. Homework Equations The Attempt at a Solution I understand the part of converting each term to each laplace, d^2y/dt to...

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...

I'm inverting this: Y = s2 + 15s + 17 / [(s+1)(s2 + 13s - 4)] I'm using PF expansion, A/(s+1) + Bs + C/(s2 + 13s - 4), I however keep on getting wrong answers, seeing how Runge-Kutta and Taylor approximation disagrees with my final equation. My final equation is...

Homework Statement Hi I am trying to solve the following system of ODE's by Laplace transforming: x' = 1 + 21y - 6x \\ y' = 6x-53y with the initial conditions x(0)=y(0)=0. Laplace transforming gives me (X and Y denote the Laplace transformed variables) sX = 1 + 21y-6x \\ sY = 6x-53y From...

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...

Hi, Part of my research, I nondimensionalized an ODE to eventually arrive at this form: sin(τλ) = q^((n+2)/(n+1)) + κq' + q'' where q' = dq/dτ The problem is of course the nonlinear q^n. n is an integer greater than 0. Is there a Laplace transform for this? Or what solutions are there for...

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...

Consider one-sided Laplace transform:$$\mathcal{L} \left \{ h(t) \right \}=\int_{0^-}^{\infty}h(t)e^{-st}dt$$ Q. Is this defined only for the functions of the form f(t)u(t)? If no, then f(t)u(t) and f(t)u(t)+g(t)u(-t-1) are two different functions with the same Laplace transform, and thus...

[SIZE="3"]L[y2] = ?

Homework Statement Solve y'' + y = f(t), y(0)=0, y'(0)=1, f(t)= (0 for 0<t<pi) (1 for pi<t<2pi) (0 for t>2pi) The Attempt at a Solution y'' + y = upi(t)-u2pi(t) s2L{y} -sy(0) -y'(0) +L{y} = L{upi(t)} -Lu2pi(t)} L{y}(s2+1) -1 = (e-pi*s/s) -(e-2pi*s/s) L{y} =...

Homework Statement Find laplace trasform of g(t) g(t) = 0 for 0<t<1, t^2 for t>1 So this can be re-written as g(t) = t2*u1(t), where u is the unit step function. By using the fact that L(uc(t)f(t-c)) = e-csF(s) i am trying to take the laplace... So in this case, f(t-c) = t2 ... so then does...

Homework Statement Is there an easier way of solving this rather than doing the integral? Find the laplace transform of: t{e^{ - t}}u(t - 1) Homework Equations The Attempt at a Solution \int_1^\infty {t{e^{ - t}}} {e^{ - st}}dt = \int_1^\infty {t{e^{ - t(1 + s)}}} dt =...

Homework Statement F{f(t)} is the Fourier transform of f(t) and L{f(t)} is the Laplace transform of f(t) why F{f(t)} = L{f(t)} where s = jw in L{f(t)} The Attempt at a Solution I suppose the definition of F{f(t)} is ∫[f(t)e^-jwt]dt where the lower integral limit is -∞...

Homework Statement I need to solve the ODE y''-y = t - tH(t-1); y(0)=y'(0)=0 Homework Equations - The Attempt at a Solution I'm fine with the process of solving the ODE, but I need a little help regarding the first t. From what I understand from lectures, all of the 't' terms need to be in...

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Homework Statement The Attempt at a Solution I can't get the jump to [e^-st(-s cost bt + b sin bt)]/(s^2+b^2) They say they have to use integration by parts but when e and a trig ratio are involved that requires tabular integration. They're obviously not using tabular...

Homework Statement The Attempt at a Solution I can understand step 2 to 3, but I can't get step 1 to 2. For simplicity sake we'll just call e^(3-s)t = N since it will = N anyway ultimately. I think the answer should be [N/3-s - 1/(3-s)^2)N - (0 - 1/(3-s)^2)0 The second term...

the questions are together with this file and my solutions are also attached. hope someone can comment on my solutions. thanks a lot and i hope i won't get any warning any more.

Hi, I was given the attached question and have given my wrong attempt at the answer. I know how to work the answer out (also shown) but I would like to know why my first attempt is wrong. Many Thanks

Hi everybody, can somewone tell me where am i wrong in this solution?(attached here) thank's

I'm new to Laplace and having slight difficulty with what looks like an obvious equation. I can do basic first and second order equations. Why is it that the seemingly easy equations are always the ones to stump you? Homework Statement \frac{dy}{dx}=-y y=2, x=0, y_{0}=2 Homework...

I have a question that has stumped me a bit, i am not sure how to use the definition to calculate it, i can use the tables, but i don't think that's what is needed. Using the definition of the Laplace transform, determine the Laplace transform of I can do it with the table but i am not sure...

Hi. Homework Statement \int\limits_0^{ + \infty } {\frac{{dt}}{{{e^{st}} \cdot (1 + {e^t})}}} Homework Equations The same as... Laplace\left[ {\frac{1}{{1 + {e^t}}}} \right] The Attempt at a Solution Found no elegant properties related to Laplace transform here. So figured my...

So I've been searching on the internet and in my textbook and I can't find a simple enough explanation of the Laplace transform of a product of functions. Is it absolutely necessary to evaluate the integral using different methods or is there an easier way?

Homework Statement Consider the following initial value problem: y''-6y'-7y=sin(9t) y(0)=-4, y'(0)=-3 I need to solve for L[y(t)]Homework Equations The Attempt at a Solution Here are the steps I've taken to solve it: L(y'')-6L(y')-7L(y)=L(sin(9t))...

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...

Hi, I've been asked to find the Laplace transform of a function and I have not the slightest clue where to begin. My professor derived the basic Laplace transforms in class(sin, cos, delta function, step function, etc), all of which I understood perfectly. However, he never really gave us an...

Homework Statement y'' + w^2y = cos(t) y(0) = 1 y'(0) = 0 w^2 not equal to 4 Homework Equations Laplace integral, transform via table/memory... Y(s) = F(s) or whatever you like to use The Attempt at a Solution s^2Y(s) - sy(0) - y'(0) + w^2Y(s) = s/(s^2 + 1). Right side is...

Homework Statement Solve the differential equation using laplace transforms. Assume zero intial conditions and that the forcing functions are zero prior to t=0 x''(t) + 6x'(t) +8x(t)=sin3t Homework Equations The Attempt at a Solution I took the laplace transform which I found to be after...

Hello, I'am looking for de correct transformation formule:\mathcal{L}[f(t).g'(t)] (and proof). I'am not looking for method to solve it by means of integrating g'(t), offcourse this a possible way. But assume that g(t) is much work to calculate. So is there a good one to one formule...

Say you find the laplace transform V(s) and want to switch it back to the time domain, once you've done this, how do you determine which parts of the total solution correspond to the complementary solution and particular solution respectively? Do you just find which parts approach zero as time...

Hi, I am trying to derive one transfer function for a system, but got stuck at a point. I want the solution to the ratio V_o(s)/V_g(s), the transfer function. V_o(s) = [a*L{(V_g)^2} - b*L{V_o * (V_g)^2} - c*V_g(s) - d/s]*z(s) In the following equation, I have: s-> lapace transform...

Heat Equation (Non Homogeneous BCs) - Difficult Laplace Transform... help! ;) Hi I'm trying to model the temperature profile of an inertia friction welding during and after welding. I have the welding outputs and have come up with a net heat flow wrt time during the process. I now want to...

Homework Statement Determine the Laplace transform: g(t) = 2*e^{-4t}u(t-1) The Attempt at a Solution Essentially we're told for a time shift we multiply the Laplace transform pair of the function (without the delay) by e^{-as} So here a = 1 (for the delay) The Laplace transform for e^{-4t}...

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 I've attached the multiple choice question Homework Equations The Attempt at a Solution I inversed laplaced the problem and i get an answer of 3 H(t-3) sin(9(t-3)) which isn't any of the options so I chose F but that was wrong. So far I've confidentally...

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 Hey guys, I've attached the question that's troubling me. I've also attached the table and formulas of Laplace transform for you convenience. Homework Equations attached The Attempt at a Solution Right now, I am thinking the best way to do this problem is...

Homework Statement We have been given a table of laplace transforms and have been asked to show them using the definition. ∫0∞e-stf(t)dt. But this one I have no clue where to begin ∫0tf(t)dt the laplace transform of this is F(s)/s. Can anyone tell me what to do with this one? Thank you...

Homework Statement Could someone please explain this to me? I have read several notes on it, but do not really follow the reasoning: The Attempt at a Solution When t = 0, -1/s*e^-st = -1/s because e^0 = 1. When t goes to infinity is the part I do not fully understand. Why...