Laplace transform Definition and 779 Threads

Homework Statement Laplace Transform of u(t-∏/2)et (u is unit step function) Homework Equations Laplace Transform Table (any) The Attempt at a Solution I tried using the Laplace transform for the unit step function and the exponential function. L{u(t-∏/2)} = e-(∏s)/2...

Homework Statement Let f(t) = t if 0<t<3 et if t>3 a. Is f(t) piece-wise continuous? b. Is f(t) of exponential order α? Either prove it by producing an M, T and α that satisfies the definition, or show that no such constants exist. c. Does the Laplace transform of f(t) exist...

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...

Homework Statement f(t)=e^(t+7)Homework Equations £{f(t)}=∫e^(-st)f(t)dtThe Attempt at a Solution so i insert my f(t) into the formula, came up with ∫e^(-st+t+7)dt using u substitution, u=t(-s+1)+7, du=(-s+1)dt so it follows that 1/(-s+1)∫e^(u)du=e^(u)/(-s+1) so I plug u back in, and should be...

Hello, What does laplace transformation exactly 'do'? If I have PDE of second order and use LT on it, what do i get to solve? ODE? or if I have ODE of second order, what do I need to solve afet transformation? How does this work? is there any rule?!

I'm working on a LaPlace transform problem. Part of it was this: -ty' I elected to do this first: (-1)\frac{d}{ds}L(y') Which I then expanded to: -\frac{d}{ds}(-y(0)+sL(y)) By the given initial conditions y(0)=0 -\frac{d}{ds}(sL(y)) So next I need to expand this out: -(L(y)+sL(y)') Now I'm...

Hello I'm struggling to understand some basics here with the laplace transform.. I'm given the laplace transform of 2/(s + 4)^4 and I need to take the inverse of this to get back to y(t) Looking at my tables the only transform similar to this is 1/(s + a)^2 I understand I can pull...

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...

Can someone explain the steps of this solution? In my linear systems class, we are doing Laplace transforms using transform tables and the properties. I can usually do the problems that closely resemble the table, but when they involve heavy algebraic manipulations, I don't know what to do...

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...

Homework Statement Solve \frac{\partial^2 v}{\partial x^2} = \frac{\partial^2 v}{\partial t^2}, x > 0, t > 0 subject to v(x,0) = 0 v_t(x,0) = 0 v(0,t) = f(t) and where v is bounded for all x > 0, by taking Laplace transforms with respect to t. Homework Equations The Attempt at...

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...