Laplace Definition and 1000 Threads

Hi all I have been working on some unique solutions to advection-diffusion type problems. One inverse Laplace transform that I seem to continue to encounter is the following: Inverse Laplace[F(s)] where F(s)=[(1/(((s-α)^2)+β)*exp(-x*sqrt(s/D))] In their classic 1959 text, Carslaw...

Homework Statement A square rectangular pipe (sides of length a) runs parallel to the z-axis (from -\infty\rightarrow\infty). The 4 sides are maintained with boundary conditions (i) V=0 at y=0 (bottom) (ii) V=0 at y=a (top) (iii) V=constant at x=a (right side) (iv) \frac{\partial...

Homework Statement y''+6'+10y=0 y(0)=2 y'(0)=1 Homework Equations The Attempt at a Solution Laplace everything and I get s^2*Y(s)-2s-1+6s*Y(s)-12+10Y(s)=0 isolate Y(s) Y(s)=(2s+13)/(s^2+6s+10) split into 2 terms, bottom can be rearranged by completing the square...

I have to try and solve the following simultaneous Laplace transform problem and don't really know which path to take can someone give me a nudge in the right direction please. dx/dt=4x-2y & dy/dt=5x+2y given that x(0)=2, y(0)=-2 this is what i have so far for dx/dt=4x-2y sx-x(0)=4x-2y...

Homework Statement Given transfer function H(s)=s^2+4 and input x(t)=sin(2t), find the ouput y(t) in time domain, and show whether bounded or unbounded. Okay, so I know L^{-1}[sin(2t)]=2/(s^2+4)=2/[(s+j2)(s-j2)] and that Y(s)=H(s)X(s)=2 Therefore, y(t)=2\delta{(t)} However, I am a...

Homework Statement f(t)= 1 if 0≤t≤1 ; 0 is t>1 find the laplace transform Homework Equations The Attempt at a Solution I know u(t)= 0 for t<0 and 1 for t≥0 I know I have to shift it and get u_a(t)=u(t-a)= 1 if 0≤t≤a, 0 if a>1 am I even going the right way? then I think...

Homework Statement f(t) = (1/(a^2))(1-e^-at - ate^-at) Homework Equations f(t) = (1/a)(1-e^(-at)) F(s) = 1/s(s+a) f(t) = t e^(-at) F(s) = 1/(s+a)^2 The Attempt at a Solution F(s) = (1/s(s+a^2)) - (1/(s+a)^2)Totally lost now, but I think this is wrong anyway, can anyone help me please. I...

∫∞x exp(N(lns-s)) ds how do integrate this when x>1 x<1 and x=1 using laplace method? the maximum point is at x=1 i have the answer for x<1 and x=1 but I am struggling for x>1 as the stationary point is no longer inside the interval.

Homework Statement f(t)=te^t, find laplace Homework Equations The Attempt at a Solution I started doing integration by parts and after doing it three times I wasn't sure if I was going in the right direction/making any progress. I'm not supposed to use a table to solve this (I...

Homework Statement Use convolution theorem to solve: \mathfrak{L} \left \{t\int_{0}^{t} \sin \tau d\tau \right \} Do not solve the integral. Homework Equations "Convolution Theorem" in textbook is stated as: \mathfrak{L}\left \{ f*g \right \}=F(s)G(s)f*g=\int_{0}^{t} \ f(\tau )g(t-\tau...

Homework Statement The switch at S is closed at time t=0 and a constant ... va−vh=v0 is applied. Use Kirchoff's laws to write 3 equations for i,i1,i2, and q(t). What is the relation between q(t) and i,i1,i2? Given that the charge on C and all currents are initially zero, find an ODE for i1(t)...

Good day to you people, I have just started learning control theory at Uni, as part of my course, and I have to admit it is quite difficult to grasp. I am starting from the basics, and I am having difficulty understanding what 's' is supposed to represent as regards the Laplace transform...

Solve $\begin{eqnarray*} {{u}_{t}}&=&{{u}_{xx}},\text{ }0<x<\infty ,\text{ }0<t<\infty \\ u(0,t)&=&\sin t,\text{ }0<t<\infty \\ u(x,0)&=&0,\text{ }0\le x<\infty . \end{eqnarray*}$ I need to apply the Laplace transform to solve this, so by applying it I get...

Hi guys, Would you help me in finding how Laplace transform is done for equation (1) in the attached image? Equation (2) is the correct solution but I don't know how we get it! I know that we can split the integration in (1) into two parts; one is from t0 to 0 and the other part is from 0...

IVP Laplace Transform Problem -- Tricky Inverse Laplace Transform Homework Statement Solve x"+x'+x=1, given x(0)=x'(0)=0 Homework Equations The Attempt at a Solution Plugged in transforms: s2*Y(s)-s*y(0)-y'(0)+s*Y(s)-y(0)+Y(s)=1/s Plugged in initial value points, simplified...

Homework Statement Hello all, Having difficulty with this one question that involves complex roots. Here it is: F(s)=\frac{s+3}{s^3+3s^2+6s+4} I tried two different ways to tackle it. First method I divided it right away: F(s)=\frac{s+3}{s^3+3s^2+6s+4}\rightarrow{s^2+6-\frac{14}{s+3}} Is there...

Hi guys, would you please help me in my question which is in the attached image? Thanks

Homework Statement Since the potential field is only a function of position, not velocity, Lagrange's equations are as follows: (Wikipedia, image 1) Homework Equations (Wikipedia, image 2) The Attempt at a Solution Now, -\frac{\partial{V}}{\partial{q_{j}}} How is speed...

Homework Statement I understand how to do initial value problems but I'm slightly stuck when the initial values are y(0) = y'(0)=0 The question is Solve: y''+3y''+2y=f(t), y(0)=y'(0)=0 where f(t) is a square wave. Homework Equations \Im{y'} =s\Im{y}-y(0)...

The problem ask me to find the tension on a capacitor after a switch has been opened. I have everything in terms of equations in s-domain and I'm sure they aren't wrong because I checked on the book. My unique problem is to understand a certain passage necessary to find the voltage knowing...

I tried doing this problem soooo many times for several days and keep failing and then I'm so worn out I can't keep thinking straight and I can't move on because of this! I'm attaching my work and it would be great if I can get back and forth feedback if necessary to find my mistake(s). The...

Homework Statement show that the Laplace transform of e^(At) = (sI - A)^(-1) \mathcal{L}\left\{ e^{At} \right\}(s) = \left(sI - A \right)^{-1} The Attempt at a Solution I find \left( e^{At} \right)_{ij} = \sum_{k=0}^{\infty} \frac{(A^k)_{ij}t^k}{k!} and since \mathcal{L}\left\{...

Hi, I'm learning about Laplace and I was wondering what substitution is when using laplace. Just say you have to find the laplace transform of {x^4 e^4x} I know what the individual transforms are = 4!//S^5 and 1/S-3 but how do you kinda smush them together, apparently that's...

So last semester, I had a Circuit Analysis course where I learned about phasors. Basically, when dealing with AC circuits, I should convert everything to the frequency domain where X = j\omega L and X = \frac{1}{j\omega C}. I feel like I understood this part really well. However, in Circuits...

Homework Statement Determine the stationary temperature distribution in the hollow sphere a<r<b where r=a is kept at T1 and r=b is kept at T2. Homework Equations \triangle u =0. But with the Laplacian in spherical coordinates. The Attempt at a Solution I think I must solve the given equation...

Homework Statement L^{-1}\{\frac{1}{(s^2+4)^2}\} Homework Equations The Attempt at a Solution I have no idea how to solve this. Any idea to being solving the problem would be appreciated.

If yes, how can we find it?

Homework Statement Consider a circle of radius a whose center is in (0,0). Let (r, \phi) be the polar coordinates and (x,y) the corresponding rectangular coordinates of the plane. Calculate the solution to Dirichlet problem (interior) for Laplace equation \nabla ^2 u =0 with the following...

Homework Statement Homework Equations The Attempt at a Solution I don't know if it is possible to use Derivative of a transform while it is on unit step function procedure. How can these questions be solved? Thank you.

The link below shows a circuit and the s-domain equation for I1(s) that I have derived; My question is on the portion of the equation containing the "(s+a)" terms. I am trying to arrive at the time-domain equation for I1(s) but instead of arriving at the Laplace transform pair shown in the...

Homework Statement could u help to find result? I don't know laplace of u^4(t)?? Homework Equations y''+4y'+5y=3u^4(t)+7(t*u(t)*δ(t-1) The Attempt at a Solution The only one i couldn t found is 3u^4(t),,

Homework Statement Find the laplace transform of f(t)=(t-5)e^{-17(t-5)}u(t-5) The Attempt at a Solution The answer I got was \frac{e^{-5(s+17)}}{(s+17)^{2}}. I thought I finally understood the process, but when I plugged it into wolfram alpha, the answer I got was different...

Homework Statement Compute the inverse Laplace transform of Homework Equations http://img267.imageshack.us/img267/696/66451772.png The Attempt at a Solution I tried using partial fraction but no luck.

So the question is: A curve rise from the origin of the xy plane into the 1st quadrant. The area under the curve from (0,0) to (x,y) is 1/5 the area of the rectangle with these points as opposite vertices. So I'm solving for f(x): So far what i have is: Area(D)=1/5 xy=integral 0 to x...

Homework Statement Say you have: EQ1: y1''*t+y1'*t+y2=0 and EQ2: y2''*t+y2'*t+y1=0 y1(0)=0,y1'(0)=0,y2(0)=0,y2'(0)=0 Homework Equations The Attempt at a Solution I can get it so far, but having both y1 and y2 really gives me fits: Eq1: Y1(-2s-1)+dY1/ds(-s2-s)=-Y2...

Hello all, Next semester I will be taking a Network Analysis course in my EE degree. Moreover, we will be utilizing numerous mathematical concepts I have not yet seen. If anyone has (preferably free) access to any of the concepts to follow that they would be willing to share, I would be...

Homework Statement The Laplace operator Δ is defined by: Δ= Show in polar coordinates r and Θ, that the Laplace operator takes the following form: http://upload.wikimedia.org/wikipedia/en/math/0/7/a/07a878276cffd0c680f3f827204aba24.png Homework Equations x=rcos(Θ), y=rsin(Θ), r ≥ 0, Θ ∈...

f(t)=\int^{c+i\infty}_{c-i\infty}F(s)e^{st}ds Why we suppose that all singularities are left from line Re(s)=c?

Homework Statement Laplace Transform of u(t-∏/2)et (u is unit step function) Homework Equations Laplace Transform Table (any) The Attempt at a Solution I tried using the Laplace transform for the unit step function and the exponential function. L{u(t-∏/2)} = e-(∏s)/2...

Homework Statement Let f(t) = t if 0<t<3 et if t>3 a. Is f(t) piece-wise continuous? b. Is f(t) of exponential order α? Either prove it by producing an M, T and α that satisfies the definition, or show that no such constants exist. c. Does the Laplace transform of f(t) exist...

Homework Statement I'm attempting to find the inverse laplace transform of (5/((2x+3)(4+x^2))) The Attempt at a Solution Here's the solution: http://www.wolframalpha.com/input/?i=inverse+laplace+transform+%285%2F%28%282x%2B3%29%284%2Bx%5E2%29%29%29 There's 3 terms in the solution and 2 are...

Homework Statement f(t)=e^(t+7)Homework Equations £{f(t)}=∫e^(-st)f(t)dtThe Attempt at a Solution so i insert my f(t) into the formula, came up with ∫e^(-st+t+7)dt using u substitution, u=t(-s+1)+7, du=(-s+1)dt so it follows that 1/(-s+1)∫e^(u)du=e^(u)/(-s+1) so I plug u back in, and should be...

Solving the Laplace equation in Cartesian Coordinates leads to the 2nd order ODEs: \frac{X''}{X}=k_1, \qquad \frac{Y''}{Y}=k_2 \qquad \frac{Z''}{Z}=k_3 In each case the sign of k_i will determine if the solution (to the particular ODE) is harmonic or not. Hence, if two people solve the...

Hello, What does laplace transformation exactly 'do'? If I have PDE of second order and use LT on it, what do i get to solve? ODE? or if I have ODE of second order, what do I need to solve afet transformation? How does this work? is there any rule?!

I'm working on a LaPlace transform problem. Part of it was this: -ty' I elected to do this first: (-1)\frac{d}{ds}L(y') Which I then expanded to: -\frac{d}{ds}(-y(0)+sL(y)) By the given initial conditions y(0)=0 -\frac{d}{ds}(sL(y)) So next I need to expand this out: -(L(y)+sL(y)') Now I'm...

[/itex][/itex]Homework Statement A battery consists of a cube of side L filled with fluid of conductivity s. The electrodes in the battery consist of two plates on the base at y = 0, one grounded and one at potential V = 12 Volts. The other sides of the battery casing are not conductive...

Hello I'm struggling to understand some basics here with the laplace transform.. I'm given the laplace transform of 2/(s + 4)^4 and I need to take the inverse of this to get back to y(t) Looking at my tables the only transform similar to this is 1/(s + a)^2 I understand I can pull...

Hello everyone, I'm currently enrolled in Control Theory at my University, and part of the coursework requires differential equations; which wouldn't be a problem, if not for the fact it's been 2 years since I've taken D.E. Anyway, over the course of the problem I ran into this little function...

Hello everyone, I'm currently enrolled in Control Theory at my University, and part of the coursework requires differential equations; which wouldn't be a problem, if not for the fact it's been 2 years since I've taken D.E. Anyway, over the course of the problem I ran into this little function...

Homework Statement F(s) = 3/(s(s^2 +2s + 5)) Homework Equations The Attempt at a Solution I have used partial fraction using coefficients. F(s) = (3/5)s - (3/5) ((s+2)/(s^2 +2s + 5)) and reduce s^2 +2s +5 by completing the square F(s) = (3/5)s - (3/5) ((s+2)/((s+1)^2 + 4))...