Laplace Definition and 1000 Threads

Laplace Error in a Circuit ! Hello as you see this circuit i want to find the v(t) across the 2ohm resistor.(VC(0-)=0) i assume A node above the capacitor , so we have (in Laplace) so i have so A=0 ! or S=-3/2 ! what can we understand about A=0 or S=-3/2 ? what is their inverse...

On MHF... Integral Caculation ... the user widapol did have some difficulties in the computation of the integral... $\displaystyle \int_{0}^{\infty} \ln^{2} (1+t)\ e^{- s t}\ dt$ (1) ... which of course is the L-Transform of the function $\displaystyle \ln^{2} (1+t)$. Remembering thye basic...

Homework Statement Hi guys! I'm basically stuck at "starting" (ouch!) on the following problem: Using the integral representation of the Bessel function J_0 (x)=\frac{1}{\pi} \int _0 ^\pi \cos ( x\sin \theta ) d \theta, find its Laplace transform. Homework Equations \mathbb{L}...

The Title pretty much says it all. I'm trying to learn how to solve the Inverse Laplace Transformation of Arctan(s/2). An equation of this sort was not explicitly covered in class and I'm having difficulty figuring where to start to solve it. If anyone could give me a general idea that would...

Homework Statement I must calculate the Laplace transform of the following function: f(x)=1 for x \in [0,1] \cap [2,3] \cap [4,5] \cap ... , f(x)=0 otherwise. Homework Equations The Laplace transform is \mathbb{L} [f(x)]=\int _0 ^{\infty} e^{-sx}f(x)dx. The Attempt at a Solution...

Homework Statement The steady state temperature distribution T(x,y) in a flat metal sheet obeys the partial differential equation: \displaystyle \frac{\partial^2 T}{\partial x^2}+ \frac{\partial^2 T}{\partial y^2} = 0 Seperate the variables in this equation just like in the...

##\mathcal{L}\{f(t)\}=F(s)## \mathcal{L}\{e^{at}\}=\frac{1}{s-a},Re(s)>a \mathcal{L}\{\sin (at)\}=\frac{a}{s^2+a^2}, \quad Re(s)>0 \mathcal{L}\{\cos (at)\}=\frac{s}{s^2+a^2},Re(s)>0 If we look at Euler identity ##e^{ix}=\cos x+i\sin x##, how to get difference converge intervals...

Homework Statement This is a practice problem for a test on Laplace transforms Find L^-1[ (9s^3+17s^2+66s+45) / (s^2+9)(s+2)^2 ] (L^-1 = inverse laplace transform) Homework Equations From Laplace transform tables: L^-1[ 1 / s-α ] = e^αt L^-1[ s / s^2+ω^2 ] = cos(ωt)...

L[sin(at)]=\frac{a}{s^{2}+a^{2}}, Re[s]>0 L[e^{kt}]=\frac{1}{s-k}, s>k L[e^{-kt}]=\frac{1}{s+k}, s<-k L[sin(at)]=\frac{1}{2i}L[e^{iat}-e^{-iat}] =\frac{1}{2i}L[e^{iat}]-L[e^{-iat}] Using the above relations =\frac{1}{2i}[\frac{1}{s-ia}-\frac{1}{s+ia}], s>ia, s<-ia The problem is...

Use the Laplace Transform of f (t) = t2 sin 7t to find the Laplace Transform of f' (t) = 2t sin 7t + 7t2 cos 7t also note that: the laplace transform of t^2 sin ωt = (6ωs^2 - 2ω^3) / (s^2 + ω^2)^3 I don't even know how to approach this so any help whatsoever would be hugely appreciated

Homework Statement An empty (charge-free) slab shaped region with walls parallel to the yz-plane extends from x=a to x=b; the (constant) potential on the two walls is given as Va and Vb , respectively. Starting with LaPlace's equation in one dimension, derive a formula for the potential at...

I have to take the inverse laplace transform of the above function. Now, I know that I can factor (s^2+5s+6) as (s+3)(s+2) and take the easy way out. However, I did it as above on a test, getting A = -1, B = -1, and C = 1. I then took the inverse laplace transform and got something involving...

\mathcal{L}\{f(t)*g(t)\}=F(s)G(s) Is there some relation between F(s)*G(s) and f(t)g(t)? ##*## is convolution.

Homework Statement I've attached an image of the question http://i48.tinypic.com/f0t0m8.jpg Homework Equations The Attempt at a Solution can't seem to make it work with the inverse - i can't implement G(s) .. any pointers on getting this solved would be great guys and girls thanks a lot

Homework Statement Laplace Transform teat Homework Equations The Attempt at a Solution http://img521.imageshack.us/img521/6449/homeworkhelp.jpg Not sure where I am going wrong. I feel like I did integration by parts incorrectly, because the anser I have boxed is not the...

Homework Statement find the partial fractions and thus the inverse of the following 6s^2-2s-11/(s-1)(s^2-1) and 7s^2+8s+16/(s+2)(s^2+3) Homework Equations answer tutor gave for the fist one was 3e^2t + 3cosht + sinht and second was 4e^-2t+3cos sqrt3t+ 2/sqrt3 sin sqrt3 The...

Hi I was just wondering when do we use the different variations of the General Fourier, Fourier Sine Transform, Fourier Cosine Transform, and Laplace Transforms. I missed my lecture and I overheard that apparently there needs to be specific boundary conditions or initial conditions which...

Homework Statement f(t) is a piecewise function: {0 0<= t< 1 {t*exp(2t) t = >1Homework Equations F(s)= L{f(t)}The Attempt at a Solution F(s)= L{t*exp(2t)} for this problem I just took the Laplace Transformer directly from the table which is: n!/ (s-a)^(n+1) and after plucking in the...

Solve Laplace's equation on a circular disk of radius a subject to the piecewise boundary condition $$ u(a,\theta) = \begin{cases} 1, & \frac{\pi}{2} - \epsilon < \theta < \frac{\pi}{2} + \epsilon\\ 0, & \text{otherwise} \end{cases} $$ where \epsilon \ll 1. Physically, this would reflect the...

This problem seems a little overwhelming at the point. I am not sure on where and how to start. Suppose that a uniform thermal gradient in the +x direction exists in a very large (i.e. effectively infinite) domain of conductivity $k_2$ such that the temperature field $u_{\infty}(r,\theta)$ can...

Solve Laplace's equation $\nabla^2u = 0$ on a $90^{\circ}$ wedge of radius $a$ subject to the boundary conditions $$ u(r,0) = 0\quad u_{\theta}\left(r,\frac{\pi}{2}\right) = 0\quad u(a,\theta) = f(\theta). $$ The standard form of the solutions for $R(r)$ and $\Theta(\theta)$ are $$...

I don't see how this $\rho = \frac{r}{R}$ helps.Let $(x_0,y_0)$ be a point in the plane, and suppose $u(x,y)$ is continuous for $(x - x_0)^2 + (y - y_0)^2 \leq R^2$, and $u_{xx} + u_{yy} = 0$ for $(x - x_0)^2 + (y - y_0)^2 < R^2$. Show that, for $0\leq r < R$, $$ u(x_0 + r\cos\theta, y_0 +...

So we have the two ODE solutions are the cosine/sine and $r^n$ since it was a Cauchy Euler type. For the steady state, the solution is just a constant since it has to have period 2pi. But with $r^n$, how with lambda equal to zero does $\ln r$ come into play? If my question is hard to follow...

I have never solved an equation in polar form. I am not sure with how to start. Solve Laplace's equation on a circular disk of radius a subject to the piecewise boundary condition $$ u(a,\theta) = \begin{cases} 1, & \frac{\pi}{2} - \epsilon < \theta < \frac{\pi}{2} + \epsilon\\ 0, &...

I want to perform the inverse of \frac s { [(s+α)^2-β^2](s^2+ω^2)} I know the conventional way is \frac s { [(s+α)^2-β^2](s^2+ω^2)}= \frac{As+B}{[(s+α)^2-β^2]}+\frac{Ds+E}{(s^2+ω^2)} s= (As+B)(s^2+ω^2)+(Ds+E)[(s+α)^2-β^2] \Rightarrow\; A+D=0,\; B+E+2\alpha...

I have this circuit which I need to solve using Laplace transforms. How would the KVL equations look? I am having trouble with them because of the mutual inductance. Thanks http://i1226.photobucket.com/albums/ee410/jean28x/CircuitMutual.jpg

Mathematica notebooks that will numerical solve for eigenvalues, density plots, Fourier coefficients, and a few other options as well. There are 7 files for 1-D and 2-D. I would like to upload them but the forum says they are invalid file types. I believe the MHB community would greatly...

Homework Statement Find f(t) for: 2\int_{0}^{t}f'(u)sin(9(t-u)du +5cos(9t), t\geq0 The Attempt at a Solution F(s)=2\frac{9(sF(s)-f(0))}{s^2+81}+\frac{5s}{s^2+81} At this point i don't know what to do with f(0) since there are no initial conditions. What do I do with it?

now say we have cos^2(3t), how would you go about computing it with the 3t? i can manage cos^2(t) but I'm not sure how to take it that one step further in the link below is what I've managed so far.. [SIZE="5"]SOLVEDI worked it out. If anyone's interested in the future, Just start it off as...

Solve Laplace’s equation $\nabla^2u = 0$ on the rectangle with the following boundary conditions: $$ u_y(x,0) = 0\quad u_x(0,y) = 0\quad u(x,H) = f(x)\quad u_x(L,y) + u(L,y) = 0. $$ How are mixed BC handled?

How to define Laplace transforms and their complex values? Homework Statement the tutorial question asks to compute the Laplace transform of cos(3t) without using linearity theorem it then asks where the laplace transform is defined in terms of complex values Homework Equations...

I've had to take diff eqtns now and I'm trying to get my head around Laplace again.. it's been a while. I can't seem to transition to the simplest step of partial fractions, my denominators are tough to figure out. If someone could point me to the next step that'd be great! Thanks a lot guys...

Homework Statement Using the t-shifting theorem, find the laplace transform of f(x) = tu(t-\pi) Homework Equations L[f(t-a)u(t-a)] = F(s)e^{-as} The Attempt at a Solution Now firstly I should state I already know the answer to the problem, the issue is getting to said answer...

Consider Laplace's equation $\nabla^2u = 0$ on the rectangle with the following boundary conditions: $$ u_y(x,0) = f(x)\quad u(L,y) = 0\quad u(x,H) = 0\quad u(0,y) = g(y). $$ How does one of the boundary conditions being defined by a derivative alter the solving of this problem? I have never...

I am trying to do laplace transform of y(t)=e^{-at}\cos (bt)\;. The answer should be: \frac {s+a}{(s+a)^2+b^2} But here is my work, I can't get rid of the -ve sign. I must be too blind to see the obvious, please help: \overline{y(s)}=\int^∞_0 e^{-(s+a)t}\cos (bt) dt\;=\; \frac 1 b...

Homework Statement d'^2 (y)/dt + 4 (dy/dt) + 4y = -7(e^(-3t)). Here I need to forced response of this differential equation using laplace transform technique. Homework Equations The Attempt at a Solution I understand the part of converting each term to each laplace, d^2y/dt to...

I have narrowed down a control systems question I am doing to the following function in the S-domain.. numerator = (5s+1) denominator = (s+3)(3s+2)(s^2) Using partial fraction expansion - I compute A = 14/63... D = 1/6... B = -2.25 And I can go no further - because both MATLAB and MAPLE...

Homework Statement By taking the Laplace transform and using the convolution theorem, obtain the solution of the integral equationHomework Equations f(t) = sin t + ∫e^(t-u)*f(u) du integral is from 0 to tThe Attempt at a Solution I used the following site as a reference for how to construct the...

Homework Statement Two semi-infinite conductor planes (like this ∠ ) have an angle β at a constant potential. Whats the potencial close to the origin? Homework Equations ∇²V = (1/r)(∂/∂r){ r ( ∂V/∂r ) } + (1/r²)(∂²V/∂\theta²) The Attempt at a Solution Trying for laplacian equation on...

[SIZE="4"]Homework Statement Show that If \phi(x,y,z) is a solution of Laplace's equation, show that \frac{1}{r}\phi (\frac{x}{r^2} ,\frac{y}{r^2} , \frac{z}{r^2} ) is also a solution Homework Equations The Attempt at a Solution let \psi= \frac{1}{r} \phi (\frac{x}{r^2}...

Homework Statement A Control system for a spacecraft platform is governed by the following equations: d²p/dt² + 2 dp/dt + 4p = θ v1 = r - p dθ/dt = .6*v2 v2 = 7*v1 All the variavles v1, v2, r, p, θ are functions in the time domain Determine the system transfer function P(s)/R(s) Homework...

maple issue -- inverse laplace transform equation from a basic series RLC circuit Pretty simple for some of you I know, but I have a laplace transform equation from a basic series RLC circuit ((sV-v(0))/L+si(0))/(s^2+sR/L+1/LC) = I(s) I want to take the inverse laplace of it, I am given all...

I'm inverting this: Y = s2 + 15s + 17 / [(s+1)(s2 + 13s - 4)] I'm using PF expansion, A/(s+1) + Bs + C/(s2 + 13s - 4), I however keep on getting wrong answers, seeing how Runge-Kutta and Taylor approximation disagrees with my final equation. My final equation is...

Homework Statement Hi I am trying to solve the following system of ODE's by Laplace transforming: x' = 1 + 21y - 6x \\ y' = 6x-53y with the initial conditions x(0)=y(0)=0. Laplace transforming gives me (X and Y denote the Laplace transformed variables) sX = 1 + 21y-6x \\ sY = 6x-53y From...

I want to find the potential of a conducting disk in space whithout laplace equation.(i know how to do that).I want to use the potential of a uniformly charged rod.because its equipotentials are ellipsoids(ellipses rotated around the rod).now a disk is a limiting case of an ellipsoid. I can't...

Hey Guys, Does anyone know where I can find a derivation of the laplace operator in spherical and cylidrical coordinates?

Solving an IVP using Laplace Transforms. HELP! Ok I'm supposed to Solve this problem using Laplace Transforms. \frac{d^2 x}{dt^2}+2\frac{dx}{dt}+x = 5e^{-2t} + t Initial Conditions x (0) = 2 ; \frac{dx}{dt} (0) = -3 so I transformed the the IVP and it looks like this s^2 x(s) - s...

I need the time domain response of this system as a unit RAMP input C(s) = ((2s²) + 20s) / ((s²) + 4s + 20) I get that the RAMP input is C(s) = A/s² G(s) And now I think I need to simplify it so I can get it into a form that's on the Laplace Transformation table but this is what I'm...

Hi all, I know that normal guassian distribution has the form exp((-x^2)/2), similarly is there any single eqn that could describe laplace distribution? -Devanand T

Good afternoon, I am a PhD student in motions of damaged ships. I am trying to find a solution of Laplace equation inside a box with a set of boundary conditions such that: ∇2\phi=0 \phix=1 when x=-A and x=A \phiy=0 when y=-B and y=B \phiz=0 when z=Ztop and z=Zbot I have tried...