Laplace transforms Definition and 177 Threads

Use the Laplace transform to solve \frac{\partial^2 y }{ \partial t^2 } = c^2 \frac{ \partial^2 y }{ \partial x^2 } for x>0, t>0 y(0,t) = t, for t>0 y(x,0) = 0, \frac{\partial y(x,0) }{ \partial t } = A, for x>0So I used the Laplace transform of a derivative, along with the initial conditions...

Homework Statement Given the equation H'(t) + u H(t - T) = 0 u > 0 Look for solutions of the form e^{rt} Show that these solutions are exponentially damped if e^{-1} > uT > 0 Find uT for which these solutions for r complex are oscillatory with growing, decaying, or constant amplitude. The...

Homework Statement Solve using Laplace Transforms \frac{dx}{dt}=x-2y \frac{dy}{dt}=5x-y Subject to x(0)=0 y(0)=0Okay. So I know that there are more efficient ways to solve this, but I missed the class in systems of Laplace Transforms and would like to get this resolved. I guess my...

Homework Statement [SIZE="6"]Inverse laplace transforms F(s)=\frac{5s-2}{s^{2}(s-1)(s+2)} Homework Equations Residue technique The Attempt at a Solution F(s)=\frac{5s-2}{s^{2}(s-1)(s+2)} = \frac{k1}{s^{2}} + \frac{k2}{s-1} + \frac{k3}{s+2} I solved for K1,K2, and K3, which...

Homework Statement We are given the following LaPlace Transformations and we are to find g(t) and h(t). L(g)(t) = 1/[(1-e^(-2s))(s-1)] L(h)(t) = (e^-s)/s(1-e^-s) Homework Equations By looking at the Table of LaPlace Transformations, the only one I found that could possibly work...

Homework Statement Derive the Laplace transform of the following functions, using first principles 3d) u(t - T) \} = 0, \ t<T \ (= 1, t>T) 3e) f(t) = e^{-a(t-T)}u(t-T) Homework Equations see above The Attempt at a Solution I know I need to derive the transform using by integration...

Find v(t) at t=800ms for the circuit in Figure 1. Ans: 802mV Writing a single node equation we have \frac{v(t)-2tu(t)}{5}+0.1\frac{dv}{dt}=0. Taking the Laplace transform we have L\left\{ \frac{v(t)-2tu(t)}{5}+0.1\frac{dv}{dt}=0\right\} . tu(t)\Rightarrow\frac{1}{s^{2}}...

Homework Statement (t − 1)^2u(t − 1) Find the Laplace transform. Homework Equations L{f(t-a)u(t-a)}(s) = e^-as F(s) The Attempt at a Solution The solution manual says take f(t) = t^2, I don't see why? Why is f(t) not (t-1)^2?

Homework Statement What is the laplace transform of e^(-t) cos 2t u(t-1) Homework Equations definition of Laplace transform: LT of f(t) = integral of f(t)e^-st dt, where limits of integration are from 0 to infinity The Attempt at a Solution since I have u(t-1) then do I just...

I am new to Derive 6 and Laplace Transforms. Is it possible to solve the closed loop gain A/B of the attached loop using Derive 6. If it is possible, can someone guide me through the steps using Derive, as the problems that lie ahead will be much more complex, and I want to use Derive in the...

Laplace Transforms on Partial Differential Equations - Non-dimensionalization too! Homework Statement The experiment described in the previous problem was analyzed from the point of view of long time \left(\frac{D_{AB}\,t}{L^2}\;>>\;1\right). We wish to reconsider this analysis in order to...

I'm posting these as images because it would be difficult to type. If this isn't allowed, please let me know. I really need help with this before tomorrow, when I have a test. Any help appreciated. Homework Statement problem here The Attempt at a Solution I completed part 1 (solution here)...

Homework Statement Using improper integrals, find the Laplace transform of f(t)=t, determining the values of s for which the transform is valid.Homework Equations The Laplace transform F(s) of a function f is defined as ∞ / F(s)= | f(t)e^(-st) dt...

Homework Statement Use a table to fing L{f(t)} for the given function f(t) defined on the interval t>=0 Homework Equations f(t)=sin(3t)cos(3t) The Attempt at a Solution Well this type of Laplace transform has got me stumped, I'm not to sure how to proceed. It doesn't seem to...

well, I found this place searching for a method to solve a laplace transform as I'm a little stuck on exactly how to do it, So I'd like to say hello, and I hope I can be of some help for someone else in the future. also, do posts here go into a moderator queue before appearing , some other...

Hello everyone, I am actually a mechanical engineering major at the University of Texas, but I thought I'd ask you kind folks for help with this problem. I apologize in advance for this being difficult to read because I don't know how to type many of these symbols. Homework Statement...

Can someone show me how to do these laplace transforms of these differentials? 1) y""-4y"'+6y" -4y'+y=0 y(0)=0, y'(0)=1, y"(0)=0, y"'(0)=1 2) y"-2y'+4y=0 y(0)=2, y'(0)=0 3) y"'+2y'+y=4e^-t y(0)=2, y'(0)=-1 4) y"-2y'+2y=cos(t) y(0)=1, y'(0)=0 the Laplace transfrom that i got for...

I began studying with a friend of mine for the FE (fundamentals of engineering) test and we began with the math section. We came across a LaPlace transform problem and we had never learned it before. Is this something I can learn relatively quickly (within the week)? I have taken calculus 1 2...

Hey guys, I am supposed to find the Laplace transform of a set of ODEs. Ive broken it down a bit and I am left with finding the Laplace transform of: (-2e^-s)/(s(s+4)(s+1)) Is this something I have to use partial fractions for? Or is there another way? I am a bit confused.

Could you please help me to do Laplace transformation ? That is an autonomous and nonlinear function on the right-hand side L{dx/dt}=L{1/1+x^a} where a is an integer other kind is in the form of delay L{dx/dt}=L{sin(x(t-\tau))} where \tau is delay, and real number

[tex] 1) \hat f(s) = 7/(s+2)(s^2+8s=41) \exp3s

Hi, I am taking a circuits analysis course currently. We are studying Laplace Transforms. I was wondering if anybody out there knows a way of bypassing all of the cumbersome complex algebra to find the partial fraction decomposition of a given function with respect to s. If not maybe...

Ok, this is the question: Assume that the Laplace transform of x(t) is given as X(s)=s / (2s^(2) + 1). Determine the Laplace transform of the following function. g(t)=x(2t-5)u(2t-5) How do I use the transform they have given me to solve this...I guess my major problem lies using time...

Hey I was wondering if someone would check my work on this problem: Note: {\cal L} = Laplace {\cal U} = Unit Step Function {\cal L} \{ \cos(2t) \,\,\, {\cal U} (t - \pi)\} =e^{-\pi s} {\cal L} \{ \cos(2(t + \pi)) \} =e^{-\pi s} {\cal L} \{ \cos(2t + 2\pi) \} =e^{-\pi s}...

Hi there, I'm trying to derive an expression for the transient response (for a step input of magnitude V), for a non-ideal inductor modeled in the schematic I have drawn. This non-ideal inductor includes its inductance ( :smile: ), a parasitic parallel resistance and a parasitic capacitance...

I need a large table of Laplace transforms, do you know any good ones? Format HTML, Pdf, Ps, Latex or Word (?) Extra question: what is the Laplace transform of a Gaussian (normal distribution), with mean m and standard deviation s (assume equal to zero for t<0)?

Can anyone explain to me the point of Laplace transforms and the shifting theorem in general?