Laplace Definition and 1000 Threads

Homework Statement Find the Laplace transform of the time function using the integral definition: g(t) = e-a(t+T)*u(t+T) Homework Equations Laplace transform definition The Attempt at a Solution After working through it, I was curious to see if the answer I received is, in...

dx/dt= -x+y dy/dt= 2x x(0)=0 y(0)=1 I'm not familiar how to solve a system like this. Somebody please help? Thanks

Homework Statement Two coaxial cylinders, radii {a,b} where b>a. Find the potential between the two cylinder surfaces. Boundary conditions: V(a,\phi) = 2 \cos \phi V(b,\phi) = 12 \sin \phiHomework Equations Solution by separation of variables: V(r,\phi) = a_0 + b_0 \ln s + \sum_k \left[...

Homework Statement y'+2y=f(t), y(0)=0, where f(t)=\left\{t, 0\leq t<0 \;and \; 0, t \geq 0 (I don't know how to do piecewise)Homework Equations Equation for initial conditions; step function: u(t-a) The Attempt at a Solution I know how to solve a differential equation with initial...

I'm struggling to learn how to find the potential using laplace solution. I know that X(x) can be rewritten in terms of C1e^kx + D1e-kx OR C1 cosh kx + D1 sinh kx OR cos kx + sin kx... but when do you know how to use which form. I understand it partially but not fully. And then how do you...

Homework Statement The attachment is the problem. Homework Equations The Attempt at a Solution I understand how to go about solving the laplace transformations but I have no idea how to start with the Heaviside functions for the 5t and the 30. What I got was 5t+30U6(t) but it turned...

Can anybody show me how to prove this Laplace transform which leads to a complimentary error function? Thanks!\int^\infty_0 \frac{\sqrt{a}}{\pi \sqrt{x} (x+a)} e^{-x} dx = e^a erfc(\sqrt{a})I don't know how to separate a factor of \sqrt{\pi} from the laplace transform.

Hi, just like to check my answer with someone for the this question calculate y"+9y=H(t-1) y(0)=0 y'(0)=-2 using laplace method H is heaviside fuction my solution: y=cos(3t)-2sin(3t)/3 + H(t-1)/9(H(t-1) + cos (3t-3) ) thanks

\nabla^2 V = \nabla \cdot \nabla V. Let me first break this down in English from my understanding: \nabla V is the gradient of a scalar function V. \nabla V is a vector field at each point P where the vector points to the direction the maximum rate of increase and |\nabla V| is the value...

Usually, we use the technique of "separation of variables" as follows: In a "separable coordinate system", we assume a separable solution \Phi=A(a)B(b)C(c) Then we obtain 3 ODEs for A(a), B(b), C(c) We note that there are actually entire families of solutions to each ODE, that happen to be...

Homework Statement I am working on solving the DE: t*x" + x' +t*x by use of the Laplace transform. Now if we just look at the first term and its transform, we have L[tx''(t)] = \int_0^\infty tx''e^{-st}\,dt = -\int_0^\infty \frac{d}{ds}\left(x''e^{-st}\right)\,dt Now in the next...

Homework Statement Y' + 8y = e^-2t*sint, with initial condition y(0) = 0 Homework Equations L{e^(-2t)sin(t)} = 1/((s+2)²+1) The Attempt at a Solution Alright so I've been working on this one for about an hour, I really don't know why but I'm having major problems with these types...

Y' + 8y = e^-2t*sint, with initial condition y(0) = 0 Alright so I've been working on this one for about an hour, I really don't know why but I'm having major problems with these types of problems, whether i don't understand how to set it up or I don't understand partial fraction...

Homework Statement solve the following differential equation using laplace transform: dy/dt+yx=0 y=20 when x=0 Homework Equations The Attempt at a Solution I took the laplace for each term L(dy/dx)= s*Y(s)-y(0) L(xy)=X(s)Y(s) subtitute back to the equation...

Homework Statement Consider the initial value problem: x'' + 2x' + 5x = δ(t - 1); with: x(0) = 0 and x'(0) = 0. Using Laplace transforms, solve the initial value problem for x(t). Homework Equations L[x''] = (s^2)*L[x] - s*x(0) - x'(0) L[x'] = s*L[x] - x(0) L[δ(t - 1)] = e^(-s)...

Homework Statement Suppose Maxwell's displacement current was left out of the Maxwell equations. Show that , in a vacuum, the magnetic field has to have the form B = grad f(r,t), where f is any function which satisfies the Laplace equation. Homework Equations curl E = - dB/dt curl B = 0...

Homework Statement i need to find the laplace transform of this equation by using the partial fraction. it is an irreducible quadratic factor that i don't really know how to solve it. Homework Equations [(s+1)^2 + 6]/[(s+1)^2 +4]^2 The Attempt at a Solution please help me, thanks. =)

Homework Statement Is there a simplified Laplace transform of The Attempt at a Solution This is actually a three part question, I was only able to solve it when q is 0 or pi/2. but i can't seem to figure out the general solution.

Solve using laplace. The diff eq is y'' + 2*y' + *y = 0 subject to y(0)=1 and y(pi)=0 Sorry if notation isn't the norm. y'' and y' and y are time (t) based functions.

Homework Statement Use Divergence theorem to determine an alternate formula for \int\int u \nabla^2 u dx dy dz Then use this to prove laplaces equation \nabla^2 u = 0 is unique. u is given on the boundary.Homework Equations u \nabla^2 u = \nabla * (u \nabla u) -(\nabla u)^2 The Attempt at...

""Invers laplace transformation"" Homework Statement Find invers laplace transform f(t) for F(s)= s /((s+a)^2 +w^2)) ? Homework Equations The Attempt at a Solution i have the final answer but i need the steps to know how i can do it exactly the final answer is ...

Homework Statement Take the Inverse Laplace Transform of: Y(s)=\frac{1}{\tau s+1}\cdot \frac{1}{s} 2. The attempt at a solution I know: L^{-1}(\frac{1}{\tau s+1})=\frac{1}{\tau}e^{\frac{-t}{\tau}} and: L^{-1}({\frac{1}{s}})=1 But how to continue?

Please anyone tell me how laplace transformation is derived. It transform a funtion into new one. Then what we get? Any example to show how it make a function easy to solve?

When comparing time and frequency domains, it is easy to imagine the meaning of the Fourier transform. In time domain, our function takes time as a parameter, and returns the value (result) of our process. When we make a Fourier transform of the same function, we take it to the frequency...

Homework Statement Consider the initial value problem y'' + 1/3y' + 4y = fk(t) with y(0) = y'(0) = 0, fk(t) = 1/2k for 4 - k < t < 4 + k 0 otherwise and 0 < k < 4. (a) Write fk(t) in terms of...

Homework Statement I need to find the Laplace transform of t*e-t*u(t-tau) 2. Homework Equations and attempt at solution I know the general form of the transform, but my problem is in the time shift of the step function. If both parts of the expression were (t-tau), then I could just...

Homework Statement Here is my issue. I am an EE student that has been part time for almost five years. I took diff eq and signals a long time ago. I am currently taking a feedback and controls class, and my lack of memory in these topics is killing my study time. I am looking for relevant...

Currently enrolled in an Electrical Engineering program, i naturally had to come across Laplace Transformation. Maths and specially calculus isn't my favourite :) What I understand is that Laplace Transform is more or less a tool used to simplify matters by defining a time based quantity in...

Hey everyone. I've got through most of a problem that involves finding an inverse laplace transform, but I am stuck at one part that requires algebraic manipulation. The function is 1/[s(2s2+2s+1)] So far I have modified it too look like .5/[s(s+.5)2 +.52](1/.5) I'm not sure how to...

Hey I'm new here. Well we're currently doing Laplace in our Maths lectures. Now the Teacher has set us a project on Laplace and we need to find some applications of Laplace Transformations. Can anyone tell me some specific areas where Laplace is applied. I remember reading somewhere it's...

Homework Statement L{4u(t-ர)cos2t} Homework Equations I have used UNIT STEP FUNCTION but could not get the result The Attempt at a Solution

Hi, I am confused between the difference between the Laplace transform and the Transfer function. I used to think that the Transfer Function was the Laplace transform of the Differential equation representation of a system, but in my readings it seems like that is incorrect - because...

im new to this forum. i really need help with the steps to solve the Laplace of sin(2t). i can put it in the formula to get the answer but I am having problems getting the steps which is what i need to follow and understand it better. if anyone can please help me with the steps it would be...

Working through a recent assignment, I've been dealing with an inverse laplace transform \mathcal{L}^{-1}\left[\frac{e^{-kds/v}}{(s+1)^2}\right] that Maple can't solve, yet I can do this by hand and WolframAlpha will solve it too. Should Maple be able to solve this (perhaps it requires extra...

Laplace Transforms Help! Homework Statement X' + 7X = 5cos2t I.C. x(0)=0 x'(0)=0

Homework Statement http://img231.imageshack.us/img231/3904/q2a.png The Attempt at a Solution Below is a screenshot of my Maple worksheet. I am currently stuck on part (a). I have taken the Laplace transform of both sides of the equation, solved for Z(s), then converted it Heaviside form, yet...

Homework Statement Find the laplace transform of f(t)=sin(4t+\frac{\pi}{3})u(t). http://img822.imageshack.us/img822/6996/codecogseqna.gif Uploaded with ImageShack.us Homework Equations Definition of laplace transform, and properties...

I have a differential equation that has to be solved with Laplace. I wish someone can provide a full answer y'' + 4y = x , 0<=x<π y'' + 4y = πe^-x , π<=x Initial Conditions: y(0)=0 y'(0)=1

Homework Statement I tried extract an s at the denominator and perform complete the square at denominator.But i feel it would be way too long to solve this problem. Gimme guide on how to tackle this problem Homework Equations...

Gimme CLue

Hi guys..:) I have a doubt regarding laplace transform. can anyone tel me... what is the physical significance of sigma+jw in it...? what interpretations we can make from sigma and jw in control theory...?

What is the Laplace Transform of f(x)=e^{bx}.sin ax?

Homework Statement It's hard to explain, I can do everything exept get the answer to what I'v pointed out below. I just don't know what order to solve it into get the correct answer, I must have tried every method except the right one! Homework Equations The Attempt at a...

Harmonic function satisfies Laplace equation and have continuous 1st and 2nd partial derivatives. Laplace equation is \nabla^2 u=0. Using Green's 1st identity: \int_{\Omega} v \nabla^2 u \;+\; \nabla u \;\cdot \; \nabla v \; dx\;dy \;=\; \int_{\Gamma} v\frac{\partial u}{\partial n} \; ds...

Hi! Im having a little (a lot) of trouble with some inverse Laplace problems. If anyone can help, I would really appreciate it! 1. 10s/(s^2+256)^2 2. 6s+6/(s+14)(s^2+4) With 1. I have tried countless ways of rearranging etc. getting (s^2+16^2)^2 to try to work it out that way... Im...

Homework Statement Could someone check my work plaese. \frac{\partial^2u}{\partial x^2}(x,y)+\frac{\partial^2u}{\partial y^2}(x,y)=0 (0<x<1, 0<y) \frac{\partial u}{\partial x}(0,y)=\frac{\partial u}{\partial y}(1,y)=0 u(x,y)\rightarrow k as y\rightarrow\infty u(x,0)=f(x) (0\leqx\leq1)...

Hey guys, I have to do a presentation for my class on the laplace transform and need to know some applications. But so far, all I can find is electrical circuit applications, not much else. So if you guys know of any others tell me about them! thanks in advance!

Homework Statement Doing some Laplace transform stuffs and I've got Y(s) = \frac{1}{(s+1)(s^{2}+2s+2)} Using the normal method 1 = A((s+1)^{2}+1) + B(s+1) I'm not sure this method is valid though as we had a complicated term (s+1)² + 1 after A. I can find A to be 1, but I don't trust my...

hi guys i cannot solve this. say that y'' + y = g(t) derive the formula y(t) = c1*cost + c2*sint + convolution of sint and g(t)

Hi all How hard is it to write a symbolic laplace solver ? (I am aware that there are many available out there, but I wanted to write one in MATLAB which doesn't use symbolic toolbox). Where can I start to get a good reference for the code ? Thank you Prabhakar