Laplace Definition and 1000 Threads

The potential on the side and the bottom of the cylinder is zero, while the top has a potential V_0. We want to find the potential outside the cylinder. Can I use the same boundary conditions as for case of inside cylinder potential? What is different?

I've been given this: x''+ x = 4δ(t-2π) The question asks: With initial conditions of x(0) = 1 and x'(0) = 0, find x(t) using Laplace transforms. I can easily get it to this: 4(sin(t-2π)u(t-2π)) But the question says "express your final solution without use of the unit step function". This is...

Homework Statement Wondering if I did this correctly.. Find the laplace transform: $$z(t)=e^{-6t}sin(\omega_{1}t)+e^{4t}cos(\omega_{2}t)$$ for ##t\geq 0## Homework Equations The Attempt at a Solution For the first part, I assume I can do this, but I'm not too sure. This is my main question...

please check my work here $\mathscr{L}[2\sin(bt)\sinh(bt)]$ I know that $\sinh(bt) = \frac{e^{bt}-e^{-bt}}{2}$$\mathscr{L}[2\sin(bt)\left(\frac{e^{bt}-e^{-bt}}{2}\right)]$...

Homework Statement Decide the inverse laplace transform of the problem below: F(s)= \frac{4s-5}{s^2-4s+8} You're allowed to use s shifting. Homework Equations The Attempt at a Solution By looking at the denominator, I see that it might be factorized easily, so I try that...

Homework Statement Find the inverse Laplace transform of the expression: F(S) = \frac{3s+5}{s^2 +9} Homework Equations The Attempt at a Solution From general Laplace transforms, I see a pattern with laplace transforming sin(t) and cos(t) because: L{sin(t)+cos(t)} =...

I took an introduction to ODEs course this past spring semester. It always bothered me where this thing came from. I did a little bit of research and found a video of a professor explaining how it is the continuous analog of an infinite sum. He did a little bit of a derivation using that...

1. why do we need to use shifted unit step function in defining second shifting theorem? 2. why don't we instead calculate laplace transform of a time shifted function just by replacing t by t-a? 3. everywhere in the books as well as internet i see second shifting theorem defined for...

Firstly, if this is an inappropriate forum for this thread, feel free to move it. This is a calculus-y equation related to differential equations, but I don't believe it's strictly a differential equation. The question I'm asking is which functions...

Homework Statement Hi. I need help to resolve the inverse laplace transform of {1/((x^2)+1)^2}2. The attempt at a solution I have tried to do: {(1/((x^2)+1) * (1/((x^2)+1)} then, convolution, sen x But, isn't working Thanks for your help :)

Homework Statement Write the Laplace equation \dfrac {\partial ^{2}F} {\partial x^{2}}+\dfrac {\partial ^{2}F} {\partial y^{2}}=0 in terms of polar coordinates. Homework Equations r=\sqrt {x^{2}+y^{2}} \theta =\tan ^{-1}(\frac{y}{x}) \dfrac {\partial r} {\partial x}=\cos \theta \dfrac...

Homework Statement I got to this while solving a physical problem, therefore it is hard for me to write the problem statement if there is none. I can write the whole physical problem here but it wouldn't make any sense. So, here is how it goes. I got to a Laplace equation ##\triangle \phi =0##...

Hi All, I'm playing around with an arduino, and have build a PID controller that controls the temperature of a light bulb, measured with an NTC. All is working fine I'm looking to get a bit more theoretical on the subject and have modeled the system in a simulink like environment. I want...

Homework Statement Ds + E / (s^2 +1)^2 Homework Equations The Attempt at a Solution Ds / (s^2 +1) + E / (s^2 +1) D[s/(s^2 + 1)^2] + E [1 / (s^2 + 1)^2]

before I go to bed(it's 11:30pm in my place), here is the last problem that I need help with find the inverse Laplace Transform $\frac{4s-2}{s^2-6s+18}$ the denominator is a non-factorable quadratic. I don't know what to do. thanks!

find the inverse Laplace of the ff: 1. $\frac{n\pi L}{L^2s^2+n^2 \pi^{2}}$ 2. $\frac{18s-12}{9s^2-1}$ for the 2nd prob I did partial fractions $\frac{18s-12}{9s^2-1}=\frac{9}{3s+1}-\frac{3}{3s-1}$ $\mathscr{L}^{-1}\{\frac{18s-12}{9s^2-1}\} =...

$\mathscr{L}\{\sin^{2}4t\}$ $\mathscr{L}\{\sin(3t-\frac{1}{2}\}$for the 2nd prob here's what I have tried $\mathscr{L}\{\sin(3t)\cos(0.5)-\cos(3t)\sin(0.5)}$ $\cos(0.5)\mathscr{L}\{\sin(3t)\}-\sin(0.5) \mathscr{L}\{\cos(3t)\}$ $\frac{3\cos(0.5)-s\sin(0.5)}{s^2+9}$ ---> is this correct? for...

please help me solve this problem $\mathscr{L}\{e^{3a-2bt}\}$ here's my attempt $\mathscr{L}\{e^{3a}\cdot e^{-2bt}\}$ from here I couldn't continue I looked up my table of transform but nothing matches the problem above. I'm not sure if the first shift formula would work here. please help...

I am stumped by an exercise in using Laplace transforms to analyze the voltage and current in simple LC tank. My issue is with the correct sign of the voltage across the capacitor ...let me pose the problem. A circuit consists of a voltage source V, 2 switches, a cap C and an inductor L. The...

As it can be read here, http://en.wikipedia.org/wiki/Laplace_transform#Relation_to_power_series the Laplace transform is a continuous analog of a power series in which the discrete parameter n is replaced by the continuous parameter t, and x is replaced by exp(-s). Therefore, computing a...

Hello, I am searching for the Laplace transform of this function u_a(y)\frac{\partial c(t)}{\partial t} where u_a(y) is the Heaviside step function (a>0). Can anyone help me? Thanks in advance! Paolo

Homework Statement Image attached. Homework Equations S-domain transformations The Attempt at a Solution Solving this using mesh analysis. I1 is straightforward : V = I1R I1 = 1.8∠75° / 2 = 0.9∠75° I2 I'm having a little trouble with. i = C dv/dt = C*V*s...

I should state, from the outset, that this tutorial is NOT going to go into any great detail about the theory and applications of Laplace transforms. Some of the aforementioned will be discussed in a cursory way, but the aim here is merely to provide a selection of proofs for common transforms...

Homework Statement ƒ(t) = 1.15t Homework Equations Standard Laplace Transform Table The Attempt at a Solution L(f(t)) = e(t * ln(1.15) = 1 / (s - ln(1.15))

Homework Statement f(s) = 6/s^2-9 Homework Equations I think f(t) = (1/b-a)(e^-at-e^-bt) The Attempt at a Solution Replace 6/s^2-9 with 6/(s-3)(s+3) a=-3 b=3 Plug in (1(6)/3-(-3))(e^-(-3)t-e^-3t) Final Result e^3t-e^-3t

Homework Statement f(s) = -5s/S^2+9 Homework Equations I think f(t) cosωt = f(s) s/s^2+ω^2 The Attempt at a Solution ω=3 Answer -5cos(3t) Can anyone tell me if I did this correctly? I think I did but just want to make sure, if not can you tell me what I did wrong? Thanks

I usually see that Laplace transform is used a lot in circuit analysis. I am wondering why can we know for sure that the Laplace and its inverse transform always exists in these cases. Thank you.

y′′+4y′+4y=f(t) where f(t)=cos(ωt) if 0<t<π and f(t)=0 if t>π? The initial conditions are y(0) = 0 , y'(0) = 1 I know that f(t)=cos(ωt)−uπ(t)cos(ωt), the heaviside equation. AND ω is allowed to vary, supposed to find the general solution, i.e. f(t) in terms of ω I think that after...

Use Laplace transfer to find the solution of the following initial value problem: y''+4y'+4y=f(t) where f(t) = cos(ωt) if 0<t<π and f(t)=0 if t>π ? Also, y(0) = 0, y'(0) = 1 Currently, I have gotten to here, but not sure how to perform inverse Laplace: (s+2)² * F(s) − 1 = [s/(s²+w²)]...

Homework Statement a) Determine power series ##\sum _{n=0}^{\infty }a_nt^n## if you know that its laplace transformation is ##-s^{-1}e^{-s^{-1}}## b) Determine function ##g## that this power series will be equal to ##J_0(g(t))##Homework Equations The Attempt at a Solution Hmmm, I am having...

Homework Statement Let ##y_1^{'}+y_1=y_2##, ##y_2^{'}+5y_2=y_3##, ##y_3^{'}+y_3=f## and ##y_1(0)=y_2(0)=y_3(0)=0##. Find ##Y_1(s)## in terms of ##F(s)##. Homework Equations The Attempt at a Solution I am completely lost here. I tried to rewrite the system so that I would...

Homework Statement I had a question in my midterm, it was to find inverse laplace tansform of: (4s+5) / (s^2 + 5s + 18.5) Where ^ denotes power. Homework Equations The Attempt at a Solution My answer was to find the complex roots of equation (s^2 + 5s + 18.5) , by them...

Homework Statement Find Laplace transformation for functions ##f(t)##: a) ##5cos(7t+\pi /4)## b) ##e^{3t}sintcost##Homework Equations The Attempt at a Solution a) I know that for ##cos(\omega t)## the laplace is ##\frac{s}{s^2+\omega ^2}## but what can I do with that ##\pi /4## ? I believe I...

I have a set of differential equations with the basic form: dy_n/dt = t*(a_(n-1)*y_(n-1)+b(n+1)*y_(n+1)-2c_n*y_n) So the time depence is a simple factor in front of the coefficient matrix. Does this set of differential equations have closed form solutions?

Homework Statement i need to solve the laplace equation in square with length side 1 i tried to solve by superposition and i got infinite sum enen thouth i know that the answer should be finite Homework Equations 1.ψ(x=0,0≤y≤1)=0 2.ψ(y=0,0≤x≤1)=0 3.ψ(x=1,0≤y≤1)=10sin(∏*y)+3x...

Homework Statement d^2x/dt^2 - 3 dx/dt + 2x= 2e^3t give that at t=0, x=5, and dx/dt=7 Homework Equations i can't figure out how to derive the values of A, B, and C from the attempted equation solution. please help me out here. thanks The Attempt at a Solution

I'm out of college and am brushing up on Laplace Transforms. I have a problem I've solved, but I believe the solution I got is wrong and can't find my error. The problem is 2x''-x'=t*sin(t) x(0)=5,x'(0)=3 My solution... Take the Laplace Transform 2(s^2x-5s-3)-(sx-5)=2s/(s^2+1)^2...

Homework Statement The coordinates ##(x,y)## of a particle moving along a plane curve at any time t, are given by \frac{dy}{dt} + 2x=\sin 2t, \frac{dx}{dt} - 2y=\cos 2t. If at ##t=0##, ##x=1## and ##y=0##, using Lapace transform show that the particle moves along the curve 4x^2+4xy+5y^2=4...

Homework Statement Compute the inverse laplace transform of F(ks)Homework Equations The Attempt at a Solution $$L^{-1} (F(ks)) = \frac{f}{|k|} \left( \frac{t}{k} \right)$$ Correct?

Exist some conection between: $$\int_{0}^{+\infty} f(t) \exp(-st)dt\;\;(1)$$ $$\int_{-\infty}^{0} f(t) \exp(-st)dt\;\;(2)$$ ? The results, the transformations, are very similar, with some little difference in the signal. So, known the transformation (1), is possible to find the (2)?

Watching this video http://youtu.be/1JnayXHhjlg?t=5m30s, I understood the ideia the Fourier transform, that is a continuous summation of sinusoids. But now If I have amplitude and phase as function of σ and ω, the summation wouldn't be ##\sum_\sigma \sum_\omega A_{\sigma \omega} \exp(i...

Hello as you see this example and solution if we assume the R of conductor sphere is 5m and check voltage in different z we obtain(for example z=1m and z=2) and as we know in conductor we doesn't have voltage differences so this equation should be the same C=0 but voltage...

Homework Statement Find the inverse Laplace transform of F(s)=5e^(-8s)/(s2+36) Homework Equations The Attempt at a Solution I know that to find the inverse Laplace transform of this function, I start by factoring out (e^(-8s)) to end up with 5/(s^2+36), and that my final answer...

I have the following 2 problems to solve using Laplace. 1) x'' + 3x' +2x=e^(-t); with x=dx/dt=0 when t = 0 2) x'' - 2x' +10x=e^(2t); with x=0 and dx/dt=1 when t=0 Where x' is dx/dt and x'' is the second derivative against time. My attempts: 1)Using laplace I get...

hello pf! i am wondering if anyone here knows of a geometric, intuitive explanation for the laplace transform? if so, please direct me to the source of if you could, explain to me your understanding? thanks!

Hi every one. Homework Statement in french,the problem says:"déterminer la force de laplace qui s'exerce entre deux fils de courants réctilignes,indéfinis,parraléles d'intensités I et I' de meme sens".maybe in english it means:"find the laplace force that is applied between two...

1. $\displaystyle \begin{align*} y''(t) + 7y'(t) + 12y(t) &= -36H(t - 2) \textrm{ with } y(0) = 0, y'(0) = 0 \\ \mathcal{L} \left\{ y''(t) + 7y'(t) + 12y(t) \right\} &= \mathcal{L} \left\{ -36H(t-2) \right\} \\ s^2\,Y(s) + s\,y(0) + y'(0) + 7 \left[ s\,Y(s) - y(0) \right] + 12Y(s) &=...

Homework Statement $$xy'' + xy = 0$$Homework Equations y'(0) = 0, y(0) = 1The Attempt at a Solution $$ L[xy''] + L[xy] = 0$$ $$-L[-xy''] - L[-xy] = 0$$ $$-\frac{d}{dp}L[y''] - \frac{dY}{dp} = 0 $$ $$-\frac{d}{dp}(-y'(0)-py(0) + p^2Y) - \frac{dY}{dp} = 0 $$ $$\frac{d}{dp}(-p + p^2Y) +...

px = t t = s^2 $$ I = \int_0^∞ e^{-s^2}ds$$ $$I*I = \int_0^∞ e^{-s^2}ds * \int_0^∞ e^{-u^2}du = \int_0^∞\int_0^∞ e^{-(s^2+u^2)}du ds$$ $$s = rsin\theta $$ $$u = rcos\theta $$ $$r = s^2 + u^2 $$ $$ I*I = \int_0^∞\int_\alpha^\beta e^-{r^2}rdrd\theta$$ How can I find my limits of integration in...

\[ \frac{(s+1)^2}{s^2 - s + 1} \] I have simplified it down to \[ \frac{s - \frac{1}{2} + s^2 + s + \frac{3}{2}}{(s - 1/2)^2 + \frac{3}{4}} = e^{1/2t}\cos\Big(t\frac{\sqrt{3}}{2}\Big) + \sqrt{3}e^{1/2t}\sin\Big(t\frac{\sqrt{3}}{2}\Big) + \frac{s^2 + s}{(s - 1/2)^2 + \frac{3}{4}} \] but I can't...