Laplace transforms Definition and 186 Threads

Homework Statement Laplace transform: te^t*H(t-1) Homework Equations L{te^t} = 1/(s-1)^2 L{H(t-1)} = e-s/s The Attempt at a Solution Using e^(at)f(t) -> F(s-a) with..e^(1t)H(t-1) We can get, e^(-1s-1)/(s-1) = e^(-s-1)/(s-1) [I think?] Thus applying tf(t) -> -dF/ds Derive[e^(-s-1)/(s-1)]...

Hi, Laplace transforms are a fundamental tool in electrical engineering and control systems engineering. Unfortunately my University is having us read books that use Laplace Transforms, but I've never learned the theory rigorously! For example the book I'm currently reading state briefly that...

I have two questions: I had to find the Laplace transform of: t \cdot sin(t) Not by definition, using a table of transforms and the properties. I did: sin(t) = i \cdot sinh(it) = i \cdot \frac{e^{t}}{2}-i \cdot \frac{e^{-t}}{2} Then t \cdot sin(t) = it \cdot \frac{e^{t}}{2}-it \cdot...

Hi there, I have my final in my circuit analysis class tomorrow morning(at a community college, it feels like two semesters worth of content was covered in 18 weeks). Last week, the teacher went over LaPlace Transform analysis rather quickly, and then onto basic digital logic. I do not...

Homework Statement Transform the given DE to find a nontrivial solution such that x(0)=0. tx''+(t-2)x'+x=0Homework Equations The Attempt at a Solution Using L{f(t)}=-\frac{1}{t}F'(s), I got 4sX(s)+s(s+1)X'(s)=0. I see that it is separable, but I do not know how to go about separating it...

Recently in my DiffEq class, we learned how to use, and come up with, Laplace transforms. After doing my homework, I realized that Laplace Transforms are my new favorite concept in math(just beating out double/triple integrals and their applications)! The transforms just look so elegant on a...

Homework Statement y''-4y'+4y = 0 y(0)=1, y'(0)=1 Homework Equations The Attempt at a Solution This is annoying, because it feels very easy and I don't know why I am not getting the answer. Skipping the routine: s^2L{y} - s - 1 - 4sL{y} + 4 + 4L{y} = 0 (s+3) / (s^2 - 4s +...

EDIT: Nevermind I see what I did wrong near the end. Homework Statement x'' + 4x = f(t) Where f(t) is 1 if t is between 0 and π, 0 if t > π. Initial conditions are x(0) = x'(0) = 0. Homework Equations Transform of a derivative: L(f^{(n)}(t)) = s^nF(s) - s^{n-1}f(0) -...-f^{n-1}(0)...

Homework Statement I'm given the transfer function of LTI system is \frac{1}{s^2 + 4} Homework Equations H(s) = \frac{Y(s)}{X(s)} The Attempt at a Solution first of all I had to find diff. equations of the system. I found that it's y'' + 4*y = x; Then they asked to find such...

Homework Statement Rearrange f(t) using Heaviside Step Function Then Rearrange it so that the Laplace Transform can be written down Then, Write the Laplace Transform of f(t) Homework Equations The Attempt at a Solution So my first step is as follows... Using the basic Piecewise Function in...

*edit* can't upload images from phone with app for some reason, finding a computer. Using the app for the first time so hopefully this works out ok.. I've attached an image with the problem written in blue, and a complete attempt in gray. I have the answer to the question however it is...

Solve... \frac{d^2}{dt^2}G(t,t') + \omega^2G(t,t') = \delta(t-t') Solve (above) if G=0 and \frac{dG}{dt}=0 at t=0 to obtain: G(t,t')=\begin{cases} 0 & 0<t<t' \\ \frac{1}{\omega}\sin\omega(t-t') & 0<t'<t \end{cases} I'm supposed to use Laplace Transforms to figure this out. (I'm going out of...

Okay, so this is the first time I'm encountering this theorem and I'm not very strong in calculus. But I tried to understand it myself but couldn't. Convolution theorem is the one in the attachment as give in the book ( couldn't find a way to type that out easily). My doubt is if laplace(f)...

Homework Statement The problem basically asks to solve the system x'(3x-1)=36e^{6t} by using laplace transforms.The Attempt at a Solution I've started by writing it (3x-1) = \frac{36e^{6t}}{3x-1} then applying laplace transform to the left side is quite simple, we get 3X(s) - 1/s. As...

Homework Statement This is a practice problem for a test on Laplace transforms Find L^-1[ (9s^3+17s^2+66s+45) / (s^2+9)(s+2)^2 ] (L^-1 = inverse laplace transform) Homework Equations From Laplace transform tables: L^-1[ 1 / s-α ] = e^αt L^-1[ s / s^2+ω^2 ] = cos(ωt)...

Homework Statement find the partial fractions and thus the inverse of the following 6s^2-2s-11/(s-1)(s^2-1) and 7s^2+8s+16/(s+2)(s^2+3) Homework Equations answer tutor gave for the fist one was 3e^2t + 3cosht + sinht and second was 4e^-2t+3cos sqrt3t+ 2/sqrt3 sin sqrt3 The...

Hi I was just wondering when do we use the different variations of the General Fourier, Fourier Sine Transform, Fourier Cosine Transform, and Laplace Transforms. I missed my lecture and I overheard that apparently there needs to be specific boundary conditions or initial conditions which...

I have this circuit which I need to solve using Laplace transforms. How would the KVL equations look? I am having trouble with them because of the mutual inductance. Thanks http://i1226.photobucket.com/albums/ee410/jean28x/CircuitMutual.jpg

How to define Laplace transforms and their complex values? Homework Statement the tutorial question asks to compute the Laplace transform of cos(3t) without using linearity theorem it then asks where the laplace transform is defined in terms of complex values Homework Equations...

Homework Statement Using the t-shifting theorem, find the laplace transform of f(x) = tu(t-\pi) Homework Equations L[f(t-a)u(t-a)] = F(s)e^{-as} The Attempt at a Solution Now firstly I should state I already know the answer to the problem, the issue is getting to said answer...

I have narrowed down a control systems question I am doing to the following function in the S-domain.. numerator = (5s+1) denominator = (s+3)(3s+2)(s^2) Using partial fraction expansion - I compute A = 14/63... D = 1/6... B = -2.25 And I can go no further - because both MATLAB and MAPLE...

Homework Statement A Control system for a spacecraft platform is governed by the following equations: d²p/dt² + 2 dp/dt + 4p = θ v1 = r - p dθ/dt = .6*v2 v2 = 7*v1 All the variavles v1, v2, r, p, θ are functions in the time domain Determine the system transfer function P(s)/R(s) Homework...

Solving an IVP using Laplace Transforms. HELP! Ok I'm supposed to Solve this problem using Laplace Transforms. \frac{d^2 x}{dt^2}+2\frac{dx}{dt}+x = 5e^{-2t} + t Initial Conditions x (0) = 2 ; \frac{dx}{dt} (0) = -3 so I transformed the the IVP and it looks like this s^2 x(s) - s...

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...

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!

I'm looking for "extended" tables of Laplace transforms i.e. ones which have examples beyond the basics commonly shown in tables. I have already linked to this one in another thread: http://www.me.unm.edu/~starr/teaching/me380/Laplace.pdf which is a good indicator of what I am looking for...

Back again with another problem. These transforms are difficult... Homework Statement Had to take a screenshot: http://i.imgur.com/LM38A.png The Attempt at a Solution His instructions are to take the Laplace Transform of each of Kirchhoff's laws. However, when we do, nothing useful comes...

Hi everyone, I know this should be obvious, but there's something I am just NOT getting. Imagine a simple series RC circuit with a DC source as shown in the attachment. As can be seen from the picture, I have solved the differential equation in capacitor current in the time domain. In...

Homework Statement I've attached the problem.Homework Equations L(1) = 1 /s L(t^n) = n!/s^(n+1)The Attempt at a Solution because the question only asks for X(s) I only considered the x' + x + 4y=3 equation. I applied laplace tranforms and got: s X(s) - x(0) + 1/s^2 + 4/s^2 = 3/s. since x(0) =...

Homework Statement Solve the differential equation y'' + 4y = g(t); y(0) = 2, y'(0) = 2 using Laplace transforms. The g(t) function is a piecewise function and is attached as g.jpg. Homework Equations Laplace transforms of regular and unit step/Heaviside functions. The Attempt at...

Homework Statement y'' + 4y' + 2y = u_pi(t) + u_2pi(t) y(0) = 0 and y'(0) = 0.Homework Equations the step function equation: u_c(t) = u(t-c) --> (laplace) --> e^-cs/sThe Attempt at a Solution i am having major probs with getting my head around step function probs wrt laplace transforms. What...

Homework Statement x' = 3x - 4y y' = 2x + 3y x(0) = 1 y(0) = 0Homework Equations y' = sY(s) - y(0) The Attempt at a Solution i am confused as to how to take laplace of either equation when i am left with a term i can't take the laplace of: specifically, x' = 3x - 4y sX(s) - 1 -3X(s) = -4Y(s)...

I recently have started learning Laplace transforms, it seems like its just a bunch of looking up tables. Along with having a bunch of standard Laplace transforms memorized. Is this how it usually is when dealing with transforms for the first time? I feel like I am not really even doing math...

Homework Statement y'' + 4y = sin(2t) y(0) = 1 y'(0) = 1 Homework Equations cramers ruleThe Attempt at a Solution after isolating Y(s) i end up with: Y(s) = 2 / (s^2+4)^2 + s/(s^2+4) after i do partial fraction decomposition, i get 4 equations with 4 unknowns, A, B, C and D i inserted B...

Homework Statement y' - 3y = 13cos(2t) y(0)=1Homework Equations y' = sY(s) - y(0)The Attempt at a Solution heres all my work.. i am confused as to why its not matching book solution.. i think (geussing) that I probably messing up the decomposition step..thanks for any help with this...

I attached the question along with its solution. Upon trying to find X(s), I get (s - 2)/(s^2 + 3s - 1) which is correct but after that I have to take the inverse Laplace transform and I don't know how to get the (-9/2 + sqrt(13)/2) and (-3/2 + sqrt(13)/2) parts and if someone could show me...

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 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)...

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...

I need to do a laplace transform on cos^3 t. I understand laplace but the trig is tripping me up. cos^3 t = Cos^2 t * Cos t = cos t * (cos 2t + 1)/2 (double angle formula) so i have (cos t)*(cos 2t)/2 + (cos t)/2. my book's solution says (cos t)*(cos 2t)/2 = (1/2)(cos (2t+1) + cost...

Ive attached the problem and my work in the pic. Questions: Am I even applying the taylor polynomial the correct way? (I never learned taylor series, but I was supposed to be taught in the pre-requisite class) Am I suppose to plug in c=4? I am not so sure about how the U4(t) works...

Homework Statement Hello all. First of all I should mention that this is not a homework problem. Rather, during workplace research I have come across the following two equations in a journal paper. Here, the authors state that one equation can be shown to be the Laplace Transform of the other...

I am reading a chapter on Complex Functions, Laplace Transforms & Cauchy Riemann (as part of Control theory) And I don't understand how they arrive at a particular part. [ I tried to type it out in tex, but it takes way too much time so uploaded a screenshot to flickr]...

To work out the laplace transform of exp(-as)*(1/s+5) Does convolution have to be used or can s - shifting be used. If s-shifting can be used can you please provide an example of how to use it in this case? My first though was s-shifting but then I would get exp(-as)*(1/[(s-a)+5])...

Homework Statement I (came up with)/(heard about) a way of using Laplace transforms that I didn't think about before. The problem is that it doesn't work for some reason. Look at following integral: I = \int_{0}^{\infty }sin(t)dt Say that you had no idea how to integrate something...

Ok, so I have uploaded/attached the question and the solution. I just need help understanding the solution please. I understand how to calculate the initial inverse transform, but I included it as the reference to the second part of the question regarding the y'' + 4y' = H(t-3) Can someone...

Homework Statement y''-6y+9y=2 y(0)=y'(0)=0 *Note* Professor will NOT allow use of partial fractions, so please don't use it.Homework Equations Laplace transform table Y=[y'(0)+sy(0)+ay(0)+R]/[(s^2)+as+b]The Attempt at a Solution Y=L(2)/(s-3)^2 L(2)=2/s Y=(2/s)[1/(s-3)^2]...

Hello I have a final coming up in ODE and I would like to check my answers during the exam. Does anybody know how to how to do laplace transforms/ inversions on a ti 89 titanium? I tried just typing lap(function) in my ti89 but that doesn't work. I tried searching google but couldn't find...

can anyone give me the working examples of current expressions of series RLC circuit using ramp voltage by Laplace transforms. thanks R=15, L= 0.4H, C=12uF ...voltage 5v

Homework Statement Im having trouble finding ways to manipulate equations to fit something from the table The two I'm stuck on are these 1. \frac{1}{s^{2}- 2s + 3} (\frac{1+(s^{2}+1)e^{-3\Pi S}}{(s^{2}+1)}) = Y(s) 2.\frac{1}{s^{2}- 2s + 2} (\frac{s}{s^{2}+1} + s - 2) = Y(s)...