Laplace Definition and 1000 Threads

Hi guys :) I'm looking to get a jump start on my uni course and have been going through some topics on my own before classes start in the Fall, I've reached the point of Laplace Transform and Fourier maths - and it's tough! I have a small question on an inverse laplace transform equation in...

Hi, Those of you familar with dynamic light scattering (DLS), will know that a common method used to obtain a particle size distribution is via a laplace inversion of the autocorrelation function. What I want to know is why? What does Laplace space have to do with DLS (I've only learned...

Homework Statement Use Laplace Transform to Solve IVP y"-2y'+2y=e^(-t) y(0)=0 y'(0)=1 Homework Equations [s^2*L{y}-sy(0)-y'(0)]-[2sL{y}-y(0)]+2L{y}=0 (for Homogeneous eq)The Attempt at a Solution Homogeneous Attempt: L{y}=1/(s^2-2s+2) Not sure if correct There soluton to this point is...

I have a linear equation y = -0.0563x + 0.7831 I am trying to find Laplace of this equation in Y(s)/ X(s) format. I do not know how to achieve it? Please help me. This equation describes the performance of a motor... torque vs angular speed (motor characteristic curve approximated to a...

Many texts in deriving the fundamental solution of the Laplace equation in three dimensions start by noting that the since the Laplacian has radial symmetry that Δu=δ(x)δ(y)δ(z) That all that needs to be considered is d^2u/dr^2 + 2/r du/dr = δ(r) For r > 0 the solution given is u= c1/r +...

Hello again. First off, I wasn't sure how to say this in the title but I'm not taking the inverse Laplace transform of a unit step function. I'm taking the Laplace transform of something that comes out to the unit step function. I have this question, which is a similar version of the...

Hello. I have gotten as far as to use the Laplace equation with these formulas, but I am having difficulty getting y and x to relate to each other. If requested, I can post my work, but I am sure it is fraught with mistakes. Help is very much appreciated! x' + 2y' - x - 2y = e^t x' - y' + x...

Consider one-sided Laplace transform:$$\mathcal{L} \left \{ h(t) \right \}=\int_{0^-}^{\infty}h(t)e^{-st}dt$$ Q. Is this defined only for the functions of the form f(t)u(t)? If no, then f(t)u(t) and f(t)u(t)+g(t)u(-t-1) are two different functions with the same Laplace transform, and thus...

[SIZE="3"]L[y2] = ?

This is what I got for Nabla and Laplace of plane wave. I have problems when I try to write out it with x, y, z coordinates. Can somebody help me? Thanks! http://img213.imageshack.us/img213/9532/85490316.jpg http://img528.imageshack.us/img528/6835/f41cab97f649df5431127b5.png

Hi all. I need to find the voltage across the inductor. I begin by solving for the current in the inductor. I first solved a circuit using differential equations (with mathematica) and achieved an answer for current in inductor of: iL(t) = E^(-5 t) (-0.75 + 1.25 E^(4 t) Later, I tried to...

Homework Statement Low-pass filter allows signals of low frequency to pass while attenuating high frequency signals; similarly, a high-pass filter allows signals of high frequency to pass while attenuating low frequency signals. The signals here can refer to voltage or current in the...

Homework Statement Solve y'' + y = f(t), y(0)=0, y'(0)=1, f(t)= (0 for 0<t<pi) (1 for pi<t<2pi) (0 for t>2pi) The Attempt at a Solution y'' + y = upi(t)-u2pi(t) s2L{y} -sy(0) -y'(0) +L{y} = L{upi(t)} -Lu2pi(t)} L{y}(s2+1) -1 = (e-pi*s/s) -(e-2pi*s/s) L{y} =...

Homework Statement Find laplace trasform of g(t) g(t) = 0 for 0<t<1, t^2 for t>1 So this can be re-written as g(t) = t2*u1(t), where u is the unit step function. By using the fact that L(uc(t)f(t-c)) = e-csF(s) i am trying to take the laplace... So in this case, f(t-c) = t2 ... so then does...

Homework Statement http://img836.imageshack.us/img836/9994/27794040.jpg The Attempt at a Solution Here is the circuit I re-drew: http://img403.imageshack.us/img403/6752/dsc0048ga.jpg Working out: http://img857.imageshack.us/img857/5633/dsc0049mo.jpg I got the denominator correct, but my...

Homework Statement Problem reads: find inverse Laplace transform of f(t) of F(s)=(2s+3)/(s(s2+7s+10) What is the value of the function f(t) at t=0 and t=∞?Homework Equations Inverse laplace transformThe Attempt at a Solution I solved F(t) down to F(t)= .3/s+0.166/s+2-0.465/s+5 thus lead me to...

Hello , can anyone help me solve this using laplace ? mx'' + cx' + kx = 0 , x(0)=0 , x'(0)=0 , m > 0 , c > 0 , k > 0 and c^2-4km > 0 thanks in advance for your answer.(first time using this forum)

Homework Statement Is there an easier way of solving this rather than doing the integral? Find the laplace transform of: t{e^{ - t}}u(t - 1) Homework Equations The Attempt at a Solution \int_1^\infty {t{e^{ - t}}} {e^{ - st}}dt = \int_1^\infty {t{e^{ - t(1 + s)}}} dt =...

Homework Statement F{f(t)} is the Fourier transform of f(t) and L{f(t)} is the Laplace transform of f(t) why F{f(t)} = L{f(t)} where s = jw in L{f(t)} The Attempt at a Solution I suppose the definition of F{f(t)} is ∫[f(t)e^-jwt]dt where the lower integral limit is -∞...

Homework Statement I need to solve the ODE y''-y = t - tH(t-1); y(0)=y'(0)=0 Homework Equations - The Attempt at a Solution I'm fine with the process of solving the ODE, but I need a little help regarding the first t. From what I understand from lectures, all of the 't' terms need to be in...

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Homework Statement The Attempt at a Solution I can't get the jump to [e^-st(-s cost bt + b sin bt)]/(s^2+b^2) They say they have to use integration by parts but when e and a trig ratio are involved that requires tabular integration. They're obviously not using tabular...

Homework Statement The Attempt at a Solution I can understand step 2 to 3, but I can't get step 1 to 2. For simplicity sake we'll just call e^(3-s)t = N since it will = N anyway ultimately. I think the answer should be [N/3-s - 1/(3-s)^2)N - (0 - 1/(3-s)^2)0 The second term...

Use of Laplace Transforms! What is the use of Laplace transforms in differential equations? I mean, why are they used? And can you please explain the "s" domain in the Laplace Transform! I studied that it is a variable in the complex plane! But, i want to grow upon that! Please help!

Homework Statement Homework Equations For a capacitor: i=C(de/dt) The Attempt at a Solution Using Kirchhoff's current law at the note above the resistor R2 I get the following equation, which I believe is right: C(e0' - ei') + (e0 - ei)/R1 + e0/R2 = 0 Then, since the source has a...

How do I take the inverse laplace transform of something that looks like this? It's part of a larger piecewise-defined second order differential equation, but this is the part I'm stuck on. (-4s-1)/(4s^2 + s + 4) Completing the square doesn't work for the bottom, so I figure I need to...

Homework Statement Homework Equations Laplace's transforms. The Attempt at a Solution Okay, so applying the Laplace on both sides yields: s^2Y(s) - sy(0) - y'(0) + 2sY(s) - 2y(0) + 10Y(s) = ? + 13 / s - 1 Is e^{-2s} / s the Laplace \delta(t - 2)? Our instructor gave us the result of...

the questions are together with this file and my solutions are also attached. hope someone can comment on my solutions. thanks a lot and i hope i won't get any warning any more.

I'm trying to find the Transfer function of the circuit below so that I can draw the Bode plot for it. I chose to use Laplace because I think it made it a little simpler. My equations so far: KVL of Left Loop: EQUATION1 Vs=I1(900+1800)-900I2 KVL of Right Loop: EQUATION2...

Hi, I was given the attached question and have given my wrong attempt at the answer. I know how to work the answer out (also shown) but I would like to know why my first attempt is wrong. Many Thanks

Hi everybody, can somewone tell me where am i wrong in this solution?(attached here) thank's

1. Homework Statement [/b] [b] I'm required to find the current i0(t), i wrote KVL equations for each loop, I0 can be expressed interms of i1 and i3, i3 being the current source on the right. i managed to get the solution down to the following : i0 = (s + 4)/(3*s^2 + 4*s + 1) I...

Homework Statement ## \frac{\partial^2 V}{\partial x^2} +\frac{\partial^2 V}{\partial y^2} = 0 ## it's defined for ##V=0 ## for ## x=0, 0<y<b##, ## x=a, 0<y<b##, ## y=0, 0<x<a## ##V=V_0 x/a ## for ## y=b, 0<x<a## Homework Equations None. The Attempt at a Solution I've got ##V(x,b) =...

Homework Statement I(s)=\frac{2}{s^2 + s} Convert this to the time domain The Attempt at a Solution Step 1 - Divide by s I(s)=\frac{\frac{2}{s}}{s + 1} Step 2 - Substract and add 1 to create new fractions I(s)=\frac{\frac{2}{s}-1+1}{s + 1} Step 3 - Split into new fractions...

I'm new to Laplace and having slight difficulty with what looks like an obvious equation. I can do basic first and second order equations. Why is it that the seemingly easy equations are always the ones to stump you? Homework Statement \frac{dy}{dx}=-y y=2, x=0, y_{0}=2 Homework...

Homework Statement laplace inverse of (40/(s^2+4s+5)^2)? Homework Equations I completed the square in the denominator to get 40/((s+2)^2+1)^2 I know that I will get cosines and sines from the shape of it in the laplace inverse; however I'm stuck. The Attempt at a Solution

Homework Statement Given transfer function : H(s)=Vo/V1=(10/s)/(4+0.4s+(10/s)) and the input voltage is given as V1=10(u(t)-u(t-0.1))V. Use the convolution integral to find Vo for t>=0.1 Homework Equations convolution integral..its hard to write and laplace table The Attempt at a...

Homework Statement Using the laplace transform technique, solve the ordinary differential equation: d2y/dt2+4.2dy/dt+4.5y=0 initial conditions: y(0)=1 and y'(0)=1 Homework Equations From laplace tables: d2y/dt2=s2Y-sy(0)-y'(0) dy/dt=sY-y(0) [b]3. The Attempt at a Solution...

I have a question that has stumped me a bit, i am not sure how to use the definition to calculate it, i can use the tables, but i don't think that's what is needed. Using the definition of the Laplace transform, determine the Laplace transform of I can do it with the table but i am not sure...

Hi. Homework Statement \int\limits_0^{ + \infty } {\frac{{dt}}{{{e^{st}} \cdot (1 + {e^t})}}} Homework Equations The same as... Laplace\left[ {\frac{1}{{1 + {e^t}}}} \right] The Attempt at a Solution Found no elegant properties related to Laplace transform here. So figured my...

Hi, When can I assume that the solution the laplace equation (or poisson equation) is radial? That is, when can I look only at (in polar coordinates) \frac{\partial u^2} {\partial^2 r} + \frac{1}{r} \frac{\partial u} {\partial r} = f(r,\theta) instead of \frac{\partial u^2} {\partial^2 r}...

Homework Statement C = 4 μF L = 0.2 Hy E is DC current. No internal resistance. Write an expression the the laplace plane transfer function, that relates current (that flows through resistor R) to the voltage E. (There is another question. I will just address the first one for...

Homework Statement I have this lowpass circuit which I have transformed to the S-domain. The circuit is to be exposed to a unit step, and then I shall convert the transient response to the time domain. Here's the transfer function of the lowpass circuit: H(s) = \frac{\frac{1}{LC}}{s^2 +...

Maybe I am just being stupid, but I don't understand why in the Laplace inversion formula (\mathcal{L}^{-1} F)(t) = \frac{1}{2\pi i} \int_{\sigma-i\infty}^{\sigma+i\infty} e^{st} F(s) ds the contour of integration must be chosen so that \sigma is greater than the real part of all...

So I've been searching on the internet and in my textbook and I can't find a simple enough explanation of the Laplace transform of a product of functions. Is it absolutely necessary to evaluate the integral using different methods or is there an easier way?

Homework Statement I have two problems i can't figure out , laplace inverse of 1/(s^2-6s+10) and laplace inverse of s/(s+1)^2 Homework Equations I use the table of laplace transforms in my book The Attempt at a Solution For the first one i did the quadratic formula to solve...

I need a physical explanation of s domain..Is s-domain a higher dimensional plane..?

Homework Statement Consider the following initial value problem: y''-6y'-7y=sin(9t) y(0)=-4, y'(0)=-3 I need to solve for L[y(t)]Homework Equations The Attempt at a Solution Here are the steps I've taken to solve it: L(y'')-6L(y')-7L(y)=L(sin(9t))...

Homework Statement Hi all, I'm struggling to find the Inverse Laplace transform of the following function: F(s) = (1+ 4e(-s) - 5e(-3s)) / s(s2 + 11s + 55), where F(s) is a Laplace transform Solution should be in terms of complex exponentials and unit step functions. Homework EquationsThe...

Hi all, I'm struggling to find the inverse Laplace transform of the following function: F(s) = (1+ 4exp(-s) - 5exp(-3s)) / s(s^2 + 11s + 55)Any help is appreciated. Thanks