Laplace Definition and 1000 Threads

Just want to verify Laplace equation in rectangular coordinates that: \nabla ^2 \vec E = 0 \Rightarrow\; \nabla^2 \vec E = \left ( \frac {\partial^2}{\partial x^2} +\frac {\partial^2}{\partial y^2} +\frac {\partial^2}{\partial z^2} \right ) ( \hat x E_x +\hat y E_y + \hat z E_z) = 0 \hbox...

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...

"physical" interpretation of the Laplace operator Is there a "physical" interpretation of the Laplace operator, much like there exists a physical interpretation of the divergence and curl?

Homework Statement According to the de Moivre Laplace theorem \binom{n}{k}p^{k}q^{n-k}\approx\frac{1}{\sqrt{2\pi{}npq}}e^{-\frac{(k-np)^{2}}{2npq}} For p=q=1/2 this translates nicely into an approximation for the binomial distribution by the normal distribution (the +1/2 is a...

Homework Statement y''-6y+9y=2 y(0)=y'(0)=0 *Note* Professor will NOT allow use of partial fractions, so please don't use it.Homework Equations Laplace transform table Y=[y'(0)+sy(0)+ay(0)+R]/[(s^2)+as+b]The Attempt at a Solution Y=L(2)/(s-3)^2 L(2)=2/s Y=(2/s)[1/(s-3)^2]...

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 +...

Homework Statement (quick sketch of part i. yes i know the graph should specifically end at t=4 lol) Homework Equations u(t-a) = 0 for t>a = 1/2 for t=a = 1 for t>aThe Attempt at a Solution i'm having trouble solving part (ii). i remember a friend of mine saying something like "start with...

Hi guys, needing a bit of help understanding laplace transformations. Homework Statement 1. f(t) = (t-4)u(t-2) 2. g(t) = (2e^-4t)u(t-1) 3. h(t) = 5 cos(2t-1)u(t) Homework Equations Laplace transform table. The Attempt at a Solution So basically I am given the laplace...

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 Hi all came across this problem whilst doing some revision and i can't work out the answer Solve the following equation with laplace transformation Homework Equations y''+16y = f(t) = { 1 t < pi ] with y(0) = 0 and y'(0) = 0 _____________{ 0 t >= pi ]...

Hello I have a final coming up in ODE and I would like to check my answers during the exam. Does anybody know how to how to do laplace transforms/ inversions on a ti 89 titanium? I tried just typing lap(function) in my ti89 but that doesn't work. I tried searching google but couldn't find...

can anyone give me the working examples of current expressions of series RLC circuit using ramp voltage by Laplace transforms. thanks R=15, L= 0.4H, C=12uF ...voltage 5v

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...

Is this problem possible? Solve the initial value problem x''(t) + 6x'(t) + 9x(t) = f(t); x(0) = N, x'(0) = M I get to X(s)=(F(t)+Ns+6N+M)/(s^2+15) and don't know where to go from here. Any help would be appreciated.

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...

Homework Statement Im having trouble finding ways to manipulate equations to fit something from the table The two I'm stuck on are these 1. \frac{1}{s^{2}- 2s + 3} (\frac{1+(s^{2}+1)e^{-3\Pi S}}{(s^{2}+1)}) = Y(s) 2.\frac{1}{s^{2}- 2s + 2} (\frac{s}{s^{2}+1} + s - 2) = Y(s)...

Solve Piecewise Equation with Laplace (Problem Solved ty) Homework Statement Solve the initial value problem: v''=(1/3)v-| sin t for t in [0,pi/2] | 0 for t in [pi/2,infinity) v(0)=v'(0)=0 Homework Equations N/A The Attempt at a Solution First I...

Homework Statement Solve the initial value problem | x'=x+y | y'=-x+y x(0)=y(0)=1 Homework Equations N/A The Attempt at a Solution This is actually a solved problem with a too many details missing. You have to set up the equation as | sX(s)-x(0)=X(s)+Y(s) |...

[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...

\documentclass[12pt,a4paper,twoside]{article} \usepackage{amssymb,amsmath,amsbsy,amscd,fancyhdr} \usepackage[mathscr]{eucal} \usepackage{tikz} \usepackage{graphicx,cite,xcolor,comment,soul,ulem} \begin{document} I met some problem in the following integration; does anyone know how to...

I am looking for inverse Laplace transform techniques with repeated roots. Example (10-4s)/(s-2)^2

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 do a laplace transform on a given non homogeneous equation. to eventually find out y Homework Equations i don't think the equation is needed. however this non homogeneous equation is equal to Ae^kt The Attempt at a Solution well. i applied the laplace to the...

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...

Homework Statement I had to solve an IVP using laplace transforms. the answer should be the laplace inverse of: (1-2e^(-s/2)+2e^(-s)+se^(-s))/((s^2)(1-e^(-s))(s^2+10s+14)) Homework Equations The Attempt at a Solution i tried partial frac. decomp. and failed miserably. I also...

Can someone explain Laplace transformations! i don't understand ittttt. [edit] sorry. i hadnt even heard of laplace transformations until i found it in my assignment. basically i want to know how to use them so, some simple, well explained examples perhaps?

Homework Statement water potential=-KH=-x^3y+xy^3+5. Is this a solution to the Laplace equation and is yes, show how Homework Equations LaPlace equation= Partial derivitive^2 of H/partial deriv x^2+partial deriv^2H/partial deriv y^2=0 The Attempt at a Solution I have absolutely no...

Homework Statement f(t) = {0, if t<4 and (t-3)^3 if t\geq4 The Attempt at a Solution I feel like its pretty basic but i can't get it down I have u(t-4)(t-4)^3 Can i change it to u(t-4)^4? Then do i multiply it out and take the laplace? If someone can work it out for me that would...

Hi everybody, I just want to know, anybody has any information or sources about the method of Finite-Integral-Transform method in order to solve the Laplace Equations. I couldn't find this topic in any texts, mostly they just introduce the method of SOV or Fourier Integral Transform. I...

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...

Homework Statement What is that oscillatory component? And is my answer for the following correct? x(t) = u(t) H(s) = \frac{R}{R + sL} y(t) will contain oscillatory component if R > \frac{1}{L} True or False? Homework Equations Basic Laplace Transform: u(t) \longrightarrow...

Homework Statement [PLAIN]http://img340.imageshack.us/img340/8508/circuit.png Find V2(s)/V1(s) (Laplace transform domain) Homework Equations KCL, capacitor equation. The Attempt at a Solution \frac {-V_2}{R} + \frac {V_1-V_2}{R} + C \frac {d(V_1-V_2)}{dt}=0 But in Laplace domain it follows...

Homework Statement I need to write ampere's law (differential form) in the form of Laplace equations / Poisson equations and then solve them numerically using Matlab. Homework Equations Del x H = J The Attempt at a Solution pls see my attachment I need help from someone who is...

Homework Statement F(s) = (2s2 + 20s + 36) / (s3 + 6s2 + 9s) Homework Equations L[e-at] = 1 / (s + a) L-1[(s+a) / ((s+a)2 + w2)] = e-atcos(wt) L-1[w / ((s+a)2 + w2)] = e-atsin(wt) The Attempt at a Solution Factored the top by 2 and the bottom by s, but the rest of the top seems...

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...

This is my first time posting on these boards, so forgive me if I am posting incorrectly or in the wrong forum. I have been able to successfully work through problems with forcing functions of constant value "steps", but am having trouble working with those with linear portions of the...

I do not have trouble doing these types of problems if the domains are not equalities. However for this type of problem.. f(t)= 0 , t=2 t , t\neq 2 (I do not know how to do piecewise function in latex) I figured this is on the right track... t-tu_{2}(t)+2tu_{3} I have a problem...

Homework Statement ((d^2)x)/(d(t^2)) + 5(dx/dt) + 6x = f(t) f(t)=3 for (0<=t<6) f(t)=0 for t>=6 Homework Equations This I am not sure of, this is my question. Would I use the Second Order Differential equation to do this problem: L{((d^2)f)/(d(t^2))} = (s^2)F(s) - sf(0") -...

Homework Statement I'm working on some Differential Equations homework and I'm stuck. The question is apply the translation theorem to find the Laplace transform. f(t) = e^(-t/2)cos2(t-1/8π) I know how to apply the method, I just need to figure out how to transform the cosine...