Laplace Definition and 1000 Threads

Homework Statement "Use Laplace transforms to solve the initial value problem" from section 4.2 in Elementary Differential Equations (6th ed.) Edwards & Penny x'' + x = cos3t; x(0) = 1 & x'(0) = 0 Homework Equations L{coskt} = s/(s²+k²) Apparently the answer is...

Hello, I'm trying to solve the following problem: \nabla^2 p = 0 \frac{\partial p}{\partial y}(x, y_{bot}) = \frac{\partial p}{\partial y}(x, y_{top}) = 0 \frac{\partial p}{\partial x}(x_{left}, y) = \frac{\partial p}{\partial x}(x_{right}, y) = C_0 which is the laplace equation...

can someone please help me find the inverse laplace transform of the following: http://www.webpagescreenshot.info/img/694286-34201141544am.png i do not know how to solve for this due to the e^-20s shift in the denominator... is there a way to change this function to make it easier to solve?

Hi All, This is not a homework question, I am just trying to be come quicker at integrating by parts, when performing Laplace Transforms. My textbook gives a basic example for performing the Laplace Transform of the variable t, to the transformed variable of s for the equation...

Homework Statement I'm considering Laplace's equation in 2D, written in circular polar coordinates (so that's u_rr + 1/r*u_r + (1/r^2)*u_theta,theta). I've worked out what all the seperable solutions are. My question is: is this set of seperable solutions complete. (That is, can all...

Dear Sir/Madam, Who knows the original publication of Laplace transformation by Laplace? Which journal and what "Title"? Recently I was recognized this problem when one of my student asked me this problem. I try to find it, but it failed to get it.

What is the laplace transform of a function that is 1 from 0 to 10 and 0 elsewhere? I know that this can be represented by the step function U(10-t)U(t)...but how do i find the laplace transform of this?

Homework Statement Find the inverse laplace tansform of this http://webwork.math.umass.edu/webwork2_files/tmp/equations/fe/0f481f24ae927e11e80569093b71321.png My question is can i pull out the e-9s and just find the inverse of \frac{1}{s2-1s+20} I broke it up into...

So, the definition of Laplace transform is: \int_{0}^{\infty} e^{-st} f(t) dt what if: f(t) = g(t)exp\Big[-\int_{0}^{t}g(t')dt'}\Big] Or, in words: if the function being transformed is itself a function of an integral. This seems somewhat tough, but maybe I just...

Hi, all. I am doing an inverse Laplace transform and meeting some difficulty. InverseLaplaceTransform[1/(Sqrt[s]+a)]. Using Mathematica I found the result, however, I failed to prove it. I know it should be like \frac{1}{2\pi i}\int_{\gamma-i\infty}^{\gamma+i\infty} \frac{1}{\sqrt{s}+a}ds...

I have two subsystems that I'm trying to transform into the frequency domain, and trying to obtain the transfer function for each. I have an equation (for system 1) m\ddot{x} -k(x2-x1) - b*\dot{x}1 = f Since this is for system 1, when I take the laplace transform of it, do i have x2 as...

i need help trying to find the laplace transform of te-t\delta(t) i know the laplace transform of te-t is 1/(s+1)2 but i don't know how to find the laplace transform of a product with the Dirac delta

Homework Statement Find inverse Laplace transform of: s/((s^2)+1)^2 Homework Equations The Attempt at a Solution The answer is: (t/2)sin t First shifting theorem or partial fractions don't work, I think. From a Laplace transforms table, sin at = a/((s^2)+(a^2)), which is almost...

what is the Laplace transform of sin2(t-1)U(t-1) (U is the unit step function) i got 2e-s/s2 + 4 is this correct? i'm unsure about the exponential part

i am given the Laplace transform of an impulse response function, as well as its input. i am supposed to find its output. H(s) = 1/s2 + s + 1 x(t) = sin2(t-1)U(t-1) what i have done so far is the following: i know that Y(s) = H(s)X(s) and from this i can easily find y(t) so i found X(s)...

Homework Statement I already got Q(s)=150/(s(s^2+20s+200)), then i complete the square on the quadratic. I got Q(s)=150/(s((s+10)^2+10^2))). But then i can't find the Q(t) because the equation (s+10)^2+10^2=0 dosent have roots. Or i have to use complex numbers ? So I am confused...

Homework Statement The question is solve using laplace transforms: y" - 4y = 1-2t where y(0) =0 and y'(0) = 0 Ans is: y = t/2 - 1/4 + 1/4*e^(-2t) Homework Equations http://www.stanford.edu/~boyd/ee102/laplace-table.pdf" partial fractionsThe Attempt at a Solution (s^2)Y - sy(0) - y'(0) - 4Y =...

So my professor is really bad and I've had to try to learn to learn this stuff myself. But I have no idea where to start and where to go. Problem: X(s) = \frac{3(3s+2)}{9s^{2}+12s+4}Attempt All I've been able to figure out so far is: -> X(s) = \frac{3}{(3s+2)^{2}} * \frac{1}{(3s+2)}} But...

show that L{f(t/b)} = bF(bs), b is not equal to 0 i know that L{f(t)} = \inte-stf(t) dt = F(s) so L{f(t/b)} = \inte-stf(t/b) dt any tips on how to start? thx

In this engineering course I'm taking I'm learning how to solve Laplace transforms. Now my ODE class only barely touched on this so I'm not sure if I'm doing this correct so I'd like some help pointing out where I went wrong, if I went wrong anywhere. x''(t) + 3 x'(t) + 2x(t) = 0, x(0) = 2...

Homework Statement Find the Laplace transform of f(t) x cos(t) (multiplication) if the Laplace transform of f(t) is F(s). Homework Equations The Attempt at a Solution I'm pretty sure I am supposed to use the second equation, however I do not understand how to use it. If you...

Homework Statement "The potential in the x-z plane is independent of z and given by a repeating step-function of magnitude 2(phi_0) and period 2a. The plane at y = y_0 is held at ground potential. Find the potential in teh region 0 < y < y_0." - Marion and Heald Classical Electromagnetic...

Hi, Is the final value theorem an appropriate way to deduce if a specific differential equations converges or diverges?

I wonder does anyone have a source for the derivation of the Laplace transform in print that is analogous to the derivation given in this video: https://www.youtube.com/watch?v=zvbdoSeGAgI https://www.youtube.com/watch?v=hqOboV2jgVo I've browsed booksgoogle but have really been unable to...

Homework Statement A cantilever beam has uniform load w over a length of L as described by the eq. EI y'''' = -w y(0) = y'(0) = 0 y''(L) = y'''(L) = 0 EI are constants find y(x) Homework Equations L[y^4] = S^4*Y(s) - S^3*Y(0) - S^2*Y'(0) - s*Y''(0) - Y'''(0) The...

[b]1. Homework Statement [/b A rectangular of HIJK sides is bounded by the lines x=0, y=0, x=4, y=2.whatis the Temperature distribution T(x,y) over the rectangle by using the Laplace equation, boundary conditions are: T(0,y)=0, T(4,y)=0 , T(x,2)=0, T(x,0)=x(4-x) Homework Equations...

Homework Statement Compute Y(t). Homework Equations Y(s)= (s(2s+11)+ω(8s+4ω^2))/((s^2+ω^2)(s+9)(s+2)) The Attempt at a Solution (s(2s+11)+ω(8s+4ω^2 ))/((s^2+ω^2)(s+9)(s+2))= A/(s^2+ω^2 )+B/(s+9)+C/(s+2) Every example I have looked at does not have the ω variable, but I...

Does anyone recognize this expression for the pressure: p(T,\mu) = T s^*(T,\mu) where s^* is the extreme right singularity in the Laplace transform of the grand canonical partion function. If someone knows this, I am curious in the derivation, and in what cases it is applicable. (In the...

Homework Statement Find the inverse laplace transform. (see figure attached for question as well as my attempt) Homework Equations The Attempt at a Solution I came up with a different answer than the given solution, and I can't figure out where I went wrong. We are given a...

Please help me to solve these problems in my homework. I should deliver it tomorrow.

Ok...so this isn't homework (well past that at 39!) but I'm trying to brush off the old cobwebs and solve a vehicle motion problem. Specically, I'm trying to find the Homework Statement Ok...so this isn't homework (well past that at 39!) but I'm trying to brush off the old cobwebs and...

What are the laplace transformations of y"' and y"". Any table I can find only goes up to y". Thanks.

Homework Statement Find the inverse Laplace Transform for the function, F(s) = \frac{(3s^{2}+9s+14)e^{-5s}}{s^3 + 4s^2 +7s} Homework Equations The Attempt at a Solution We are given a table of common laplace transforms that we are allowed use to without proof. First I'll...

Hello All, I am experiencing some difficulties with Laplace transform and Fourier transforms. I am summarized my understanding of my conceptual understanding would really appreciate if someone could comment on it: A continuous time domain signal can be transferred into the complex frequency...

Homework Statement I'm supposed to find a nontrivial solution to tx'' + (t-2)x' + x = 0, x(0) = 0. You don't really need to know that but just in case. I got to this point: (s+1)X'(s) + 4X(s) = 0 Now I need to separate variables to find a solution but I've been working on this for two...

I'm trying to prepare for an exam and we were warned that the Laplace transforms given to us may have Complex roots, double roots, or double complex roots. I'm comfortable with complex roots, but I can't find a problem in the textbook that deals with double roots, and I haven't used them since...

Homework Statement s2/((s2-1)(s-1)2) Homework Equations laplace tables The Attempt at a Solution I attempted the shifting method and also partial fraction method but efforts were fruitless

Homework Statement u_{tt}=u_{xx} The Attempt at a Solution Where do I start? I have this wonderful Schaums outline at hand, and by looking at similar (unfortunately unsolved problems) I can guess that the answer will be in the range of: u=F(x+iy)+G(x-iy) I'm saying something in...

Hey Guys. Im trying to find an inverse laplace transform for fraction in the laplace domain but can't find it in any of my laplace pair tables. The fraction is: 1/(s + 4)(s + 4)(s + 8) Does anybody have any suggestions?

Homework Statement The circuit below (please see attactment) shows an RLC filter circuit whereby RC = 1/2 and LC = 1/16. Determine the differential equation that describes the relationship beween the input voltage Vi(t) and output voltage Vo(t). If the initial conditions of the capacitor and...

I really appreciate if anyone could indicate me how to handle this inverse Laplace transformation (ILT): L-1[Exp(-c0*Sqrt(a(s)))/Sqrt(a(s))] where a(s)=(s2+c1s)/(c2s+c3) c0,c1,c2,c3 are all constants. I searched some literatures regarding the ILT of Exp funtions but no such form. I used...

Please help me explain how to solve this to find the unilateral laplace transform x(t)=tu(t) - (t-1)u(t-1) - (t-2)u(t-2) + (t-3)u(t-3) I know the part tu(t) as a(t) = u(t) --> 1/s then b(t) = tu(t) ---> - d/dx a(t) = 1/s^2 But for those (t-1), (t-2) in front u(t), how to solve...

Homework Statement Find the inverse Laplace Trasnform of, F(s) = \frac{s^{2}}{(s^{2} + 9)^{2}} Homework Equations The Attempt at a Solution We are given a table with a bunch of common Laplace transforms and their inverses but I can't seem to get this one. Can anyone nudge...

Homework Statement Find the Laplace Transform from the definition of f(t) = tcos(2t) Homework Equations \int e^-^s^ttcos(2t)dt The Attempt at a Solution I started by doing parts u = t du = dt dv = cos(2t)e^-^s^t dt but I get stuck on v and as far as I can tell doing parts...

Homework Statement I'm trying to take the laplace transfrom of t H(t) where H(t) is the unit step function. Also, in a separate problem I get e^{-t} H(t) - e^{-t}H(t-1) and I am wondering how to manipulate it properly Homework Equations L \{ f(t-a) H(t-a) \} = e^{as}F(s) The...

hi everyone, I am new to physics forums and am struggling with Laplace. I have been given 3 problems: a) sint-tcost -> find the laplace transform of the fiven function without using table b) 3/ s2(s2-a) -> Find the inverse laplace transform of the given function c) Ln (1 + sinx) ->...

Hello, I'm learning how to solve Laplace's equation to find Potentials in Cartesian, Cylindrical, and Spherical Coordinates and let's just say it's not going as smoothly as I'd like. In particular, I'm having difficulty with the Spherical case which involves Legendre Polynomials, Method of...

Question on Solving Laplace Equation Potentials. Hello, I'm learning how to solve Laplace's equation to find Potentials in Cartesian, Cylindrical, and Spherical Coordinates and let's just say it's not going as smoothly as I'd like. In particular, I'm having difficulty with the Spherical case...

1. find the Laplace transform of \sqrt{t/pi}cos(8t). 2. Tried to look at the tables and combine things but I'm not very sure where to start.

Homework Statement Find the Inverse Laplace Transform of \frac{200}{s^{2}+10s+200} Homework Equations The Attempt at a Solution Normaly use partial fractions to get simple functions that can be transformed using a table of transforms.