Laplace Definition and 1000 Threads

so I am working on a problem and i have a question about the step function. let's say that a decaying force is f(t). with u (t-11)= {0 if t< 11, 1 if t>=11}. the function of the force is then g(t)=[1-u(t-11)]* f(t) or g(t)=f(t)-[u(t-11)*f(t)] as i understand it. in order to do the...

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...

I was wondering if someone could help me go through a simple example in using Green's Function. Lets say: x' + x = f(t) with an initial condition of x(t=0,t')=0; Step 1 would be to re-write this as: G(t,t') + G(t,t') = \delta(t-t') then do you multiply by f(t')\ointdt' ? which I...

I need to use Laplace transforms to find the solution to this system of Heaviside functions but I'm not sure where to start because the two different x's in the system are confusing me. Should I start by taking the laplace transforms of both sides where the laplace of H(t-1) = e-s/s These...

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

I was trying to solve this partial differential equation which arose because I wanted to find a general solution to the Laplace equation in the case f=f(x,y). \frac{{\partial}^{2}f}{{\partial x}^{2}}+\frac{{\partial}^{2}f}{{\partial y}^{2}}=0 Thanks in advance.

I need to do a laplace transform on cos^3 t. I understand laplace but the trig is tripping me up. cos^3 t = Cos^2 t * Cos t = cos t * (cos 2t + 1)/2 (double angle formula) so i have (cos t)*(cos 2t)/2 + (cos t)/2. my book's solution says (cos t)*(cos 2t)/2 = (1/2)(cos (2t+1) + cost...

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...

Is it possible to obtain a general expression for the solution of laplace equation that is valid in an euclidean space with an arbitrary dimension ?

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 Find the inverse laplace transform of the equation listed: (\frac{1-e^{-sa}}{a})*(\frac{1}{s^2}-\frac{RC}{s}+\frac{sRC+R^2\frac{C}{L}-1}{s^2+s\frac{R}{L}+\frac{1}{LC}}) Homework Equations a, R, C, and L are constants. The Attempt at a Solution Completely...

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}...

Homework Statement Use Laplace transformations to solve: Y''+tY'+2Y=0, Y(0)=0, Y'(0)=1 Homework Equations Y''==>s^{2}y-sY(0)-Y'(0)=s^{2}y-1 tY'==>-(y+sy') 2Y==>2y The Attempt at a Solution The question felt pretty straightforward till I hit a rock.s^{2}y-1+y-sy'=0...

Homework Statement Any way to reduce this function for simplification? (Trying to find the reverse Laplace function) I found this function after doing a circuit analysis on a transmission line. \frac{s^2RC+sL}{s^2RC+sL+R} Homework Equations noneThe Attempt at a Solution I couldn't...

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...

Homework Statement y'' + 3y' + 2y = u_2(t); y(0)=0, y'(0)=1Homework Equations L\{u_c(t)h(t-c)\}=e^{-cs}H(s)The Attempt at a Solution I've actually tried two laplace equation with discontinuous forcing function problems. I get answers somewhat close to the back of the book, but still off. Maybe...

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...

Verify that the function U = (x^2 + y^2 + z^2)^(-1/2) is a solution of the three-dimensional Laplace equation Uxx + Uyy + Uzz = 0. First I solved for the partial derivative Uxx, Ux = 2x(-1/2)(x^2 + y^2 + z^2)^(-3/2) = -x(x^2 + y^2 + z^2)^(-3/2) Uxx = -(x^2 + y^2 + z^2)^(-3/2) +...

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)...

Ive attached the problem and my work in the pic. Questions: Am I even applying the taylor polynomial the correct way? (I never learned taylor series, but I was supposed to be taught in the pre-requisite class) Am I suppose to plug in c=4? I am not so sure about how the U4(t) works...

Homework Statement Find the inverse Laplace transform of \frac{2s+1}{s^2-2s+2}Homework Equations The Attempt at a Solution \begin{align*} L^{-1}\{ \frac{2s+1}{s^2-2s+2} \} &= 2 L^{-1}\{ \frac{s}{(s-1)^2+1} \} + L^{-1}\{ \frac{1}{(s-1)^2+1} \} \\ &= 2 L^{-1}\{ \frac{s}{(s-1)^2+1} \} + e^t...

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...

I am reading a chapter on Complex Functions, Laplace Transforms & Cauchy Riemann (as part of Control theory) And I don't understand how they arrive at a particular part. [ I tried to type it out in tex, but it takes way too much time so uploaded a screenshot to flickr]...

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)...

Assumed solution for the Laplace EQUATION?? The book I'm using says that the method of separation of variables is a must when solving the Laplace equation. OK, well they ASSUME that the solution looks like V(x,y,z) = X(x)*Y(y)*Z(z) but why can't they assume a solution of V(x,y,z) =...

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 D^2 x -2x = 2sin2t x(0) = 0 , x'(0) = 1 Homework Equations D^2 x = s^2ƒ[x] - sx(0) - x'(o) The Attempt at a Solution s^2ƒ[x] - sx(0) - x'(o) - 2ƒ[x] = 2sin2t s^2ƒ[x] - sx(0) - x'(o) - 2ƒ[x] = 4 / s^2 + 4 ƒ[x] (s^2 + 1) + 1 = 4 / s^2 +4...

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?

To work out the laplace transform of exp(-as)*(1/s+5) Does convolution have to be used or can s - shifting be used. If s-shifting can be used can you please provide an example of how to use it in this case? My first though was s-shifting but then I would get exp(-as)*(1/[(s-a)+5])...

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 I (came up with)/(heard about) a way of using Laplace transforms that I didn't think about before. The problem is that it doesn't work for some reason. Look at following integral: I = \int_{0}^{\infty }sin(t)dt Say that you had no idea how to integrate something...

Ok, so I have uploaded/attached the question and the solution. I just need help understanding the solution please. I understand how to calculate the initial inverse transform, but I included it as the reference to the second part of the question regarding the y'' + 4y' = H(t-3) Can someone...

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...