Laplace transform Definition and 752 Threads

How do I take the laplace transform of a two dimensional wave equation? I need an answer now!

Homework Statement T(x,t) is the temperature distribution for t > 0 in a semi-infinite slab occupying x > 0 T(x, 0) = T_0 e^{-ax} for x > 0 (with a positive constant) T(0, t) = T_1 for t > 0 \tau(x, s) is the Laplace transform of T(x, t) show that \tau(x, s) = \frac{T_0}{s - Ka^2}e^{-ax} +...

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}...

Homework Statement Hi, I am wondering how to Laplace transform this expression f(t)=\int^{\tau}_{0} g(\tau)f'(t-\tau)d\tau or more precisely f(t)=\int^{\tau}_{0} sin(8\tau)f'(t-\tau)d\tau The f'(t-\tau) gets me confused. Homework Equations \int^{\tau}_{0}...

For the circuit below, find the Va(s) What I have done so far: I attempted to solve using the node method when the switch is closed (t > 0) (va - v0)/R1 + C2dva/dt + va/R2 = 0 After a series of calculations I got Va(s) = (V0/C2R1)*(1/s+(1/C2R1) + (1/C2R2)) What I am unsure of is if my first...

I am given a function f(t) with it's corresponding Laplace Transform in the Frequency Domain (F(s)). I'm having a hard time wrapping my head around the product of say, L{cos(t)*f(t)}. The * is multiplication and not convolution. Must I do the integration for the Laplace transform by hand...

in this question x(t) is right sided signal so ROC should be to the right of right most pole but here they've given ROC is Re(s) >-3 but there is a pole @ -2 how is this ?

Homework Statement is it possible to find the laplace transform of f(t-b) ? i don't know if its possible, i am just trying. The Attempt at a Solution so, where integral from 0 to infinity, \int f(t-b) e-stdt let t-b = z =\intf(z) e-s(z+b)dz =\intf(z) e-sze-sbdz =e-sb f(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 Solve inital value problem: x''+2x'+x=g(t) g(t)= t 0<t<1 2-t 1<t<2 0 t>2Homework Equations Second shift theorem, Heaviside function and Laplace transforms. I denote Heaviside,functuon H(t-a), and Laplace transform with L The Attempt at a Solution I...

Hi..new here. I'm having trouble finishing off a very basic laplace transform problem. I'd greatly appreciate it if someone could show me the way. The problem is #5 from this picture: http://www.flickr.com/photos/67208468@N08/6111476312/ What I did was use the Euler's formula for sin t and I...

I am reading the book QFT II: Quantum Electrodynamics by Eberhard Zeidler. On page 32 he defines the Laplace transform as: F(s) = \int_0^{\infty}f(t)e^{ist}dt Where f is a smooth function and F is it's Laplace transform. I have changed his notation, but not the content of the formula. I...

Homework Statement Use the second shifting theorem to find the Laplace transform of f(t) = {t2, t<4 {t, t\geq4 Homework Equations L{f(t - a)u(t - a)} = e-as F(s) The Attempt at a Solution Okay so I applied the unit step function to get the equation into the form f(t)...

Homework Statement Solve the Initial value problem using Laplace transform \ddot{y} +2y = 0, y0 = C1, \dot{y} = C2 Homework Equations [s2 - sy(0) - y'(0)] + a[sY - y(0)] + bY The Attempt at a Solution s2Y - sy(0) - y'(0) + 2y = 0 s2Y + 2Y = sy(0) + y'(0) (s2 + 2)Y = s(C1) + (C2)...

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...

if say the function f(t) is 0 from 1 to 2 is 1 from 2 to 3 if i laplace transform it , for f(t) = 1, i get f(s) = 1/s so what are the limits for my s ? is it still 2 to 3? thanks!

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...

EDIT: I think all errors are fixed now. It's 1:30 AM and I'm going to bed now. Hello, I am trying to find the Laplace transform of tan(t), but I don't know if I'm getting anywhere. I can't find it in Laplace transform tables and WolframAlpha gives me an answer in terms of complex numbers...

Just a quick question...what kind of maths do i need to understand to start to get to grips with laplace tranforms? Thanks

Homework Statement Hi, I am writing a little program (I need it for my course from Theory of Reliability) and as I am neither experienced mathematician nor programmer I faced with this problem. What would this formula Look like if I would sole it for 'z' not for 'Fz' ? Homework...

hello, I'am stuying the laplace transform and have problems with understanding the follow thing my course says: lim s->+inf F(s)=lim t->0 f(t) lim s->0 F(s)=lim t->+inf. f(t) I would like to understand it because I have the feeling that this are important properties. Thank you very...

I know that there is the Bromwich integral which inverts the Laplace Transform but it requires the function to have poles. I am wondering if there is a formula for inverting a function which decays rapidly but has no poles?

Homework Statement Find the Laplace Transform of t.H(t-a) where H is the heavyside (unit step) function. Homework Equations Properties of Laplace Transforms L{t.f(t)} = -Y'(s) L{f(t-a).H(t-a)} = e-as.F(s) Maybe another one I don't know about? The Attempt at a Solution...

Homework Statement Laplace Transform of e-t sin t Homework Equations The Attempt at a Solution I have the solution, but I am unable to figure out how the denominator becomes 1/[(s + 1)2 + 1]

I've been messing around with Laplace transforms. Anyway to get to the point I arrived at a "solution" in the s domain and got stuck. I'm trying to solve for the inverse laplace transform of A: {\cal L}^{-1} \{A\} where A = F(s) e^{C_2\sqrt{-s+C_1 }} and C_1,C_2 are constants and...

Hello, We recently learned in mathematics the Laplace transform. But we didn't actually use it to solve circuits yet. I took things at my own hand and tried to figure out what's the point of Laplace transform. I figured out all that frequency and time stuff. But here is the thing. If...

i can do the majority of laplace questions that will be asked, but i don't understand how to derive the formulae, and this is a past paper question :/ could someone please walk me through this question, or give me some tips?

[Ask] How to write laplace transform in c or c++ ?? Hi Guys.. if I have a laplace transform example : T(s) = 1/s+1. It's easy to solve or write in Matlab, but how to write it in C programm ?? thanks :)

Okay so I am brushing up my Laplace transforms as an independent study and I come across this proof for the "division by t theorem". The idea proof it self I have no problems with except for the limits of the first integration, It feels like they just arbitrarily choose the limits to be from...

Homework Statement If f(t)=K + 2cost and F(s) = L{f(t)}, find all the real values of K such that \int_{1}^{2}F(s)ds = 2ln5 The attempt at a solution So L{f(t)} = L{K} + L{2cost} = (K/s) + [2/(s2 + 1)] So \int_{1}^{2}\frac{K}{s}ds + \int_{1}^{2}\frac{2s}{s^{s}+1}ds = 2ln5 After...

1. y'' -5y' + 6y = 0, y(0) = 1, y'(0) =2 3. [s^2 F(s) - s f(0) - f'(0)] -5 [F(s) - f(0)] + 6[F(s)] = 0 (s^2 +1)F(s) - (s -5)f(0) - f'(0) = 0 (s^2 + 1)F(s) - (s-5)(1) - 2 = 0 (s^2 + 1)F(s) = s -3 F(s) = (s-3)/(s^2 + 1) Here's where I'm stuck. I can't factor the denominator to...

Hi, this is my first post, and I'm not sure if I'm posting this in the right place. Homework Statement I have a 2nd order diff. equation: 3y''(t) + 2y'(t) + 5y(t) = 3 with initial values: y'(0) = 1, y(0) = 0 Homework Equations After using Laplace transform I get: Y(s) = (3 +...

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...

Hi all According to the textbook Signal and Systems by Oppenheim (2nd edition) pages 685 and 686, if the Laplace transform of x(t) is X(s) with ROC (region of convergence) R, then the Laplace transform of x(at) is (1/|a|)X(s/a) with ROC R/a. Consequently, for a>1, there is a compression...

Homework Statement L{2t u(t-1)} Homework Equations L{g(t) u(t-c)} = e^-cs L{g(t+c)} The Attempt at a Solution L{2t u(t-1)}=e^-s L{2(t+1)} L{2(t+1)}=2/s^2+2/s L{2t u(t-1)} = e^-s {2/s^2 + 2/s} i think the whole attempt is wrong , I'm getting confused in this type of...

Homework Statement just trying to get the below equation in terms of step functions, just not sure how to get the cos(t) with the same shifted variable f(t) = 0 for t<2 f(t)=cos(t) t>=2 The Attempt at a Solution this is what i got cos(t)u(t-2) just having troubles working out the...

[Solved] Laplace Transform Homework Statement \frac{d^{2}y}{dt^{2}}+4y=sin(t),\quad y(0)=0,\quad\frac{dy}{dt}(0)=0 Homework Equations Laplace transform is defined as: \mathcal{L}\{f(t)\} = \int_{-\infty}^{\infty}f(t)e^{st}dt The Attempt at a Solution...

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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 Solve the differential equation: y'' + 4y' + 4y = delta_3 (t) y(0) = 0 and y'(0) = 1Homework Equations 1) lapace [delta_a] = e^-as 2) laplace inverse [ 1 / (s+a)^n] = [(t^n-1) / (n-1)! ] *e^-atThe Attempt at a Solution so I began by taking the laplace transform of both...

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 I need to know what the laplace transform is for f(t) * u(t) More specifically, h(t) = cos(3t)*u(t) Homework Equations I know that f(t-to) * u(t-to) = e-tos * F(s)The Attempt at a Solution So, f(t) = cos(3t) F(s) = s/(s2 + 9) In the formula I gave in (2), I would...

Can some one help me to understand this: I need to use the second shifting theorem to get the Laplace transform, given: f(t) = { 4 - t2 , t < 2 ...... 1 { 0 , t >= 2 They got this: f(t) = (4 - t2)(1 - u(t - 2)) .... 2 I know that the...

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 The signal x(t) = u(t-1) - u(t-3) is the input to an LTI system with the impulse response h(t) = u(t-5) - u(t-8). the system is initially at rest. a) Compute the output y(t) of this system using convolution. b) Compute the output y(t) of this system using the Laplace...