Laplace transform Definition and 752 Threads

Hi guys..:) I have a doubt regarding laplace transform. can anyone tel me... what is the physical significance of sigma+jw in it...? what interpretations we can make from sigma and jw in control theory...?

What is the Laplace Transform of f(x)=e^{bx}.sin ax?

Homework Statement It's hard to explain, I can do everything exept get the answer to what I'v pointed out below. I just don't know what order to solve it into get the correct answer, I must have tried every method except the right one! Homework Equations The Attempt at a...

Hey guys, I have to do a presentation for my class on the laplace transform and need to know some applications. But so far, all I can find is electrical circuit applications, not much else. So if you guys know of any others tell me about them! thanks in advance!

Hi all How hard is it to write a symbolic laplace solver ? (I am aware that there are many available out there, but I wanted to write one in MATLAB which doesn't use symbolic toolbox). Where can I start to get a good reference for the code ? Thank you Prabhakar

This is some homework from my Analog Signal Processing class, it's a cool class and I've not had much trouble, but this is giving me a bit of a problem and I was hoping someone could help me see what I'm doing... Here's the problem: Sketch, Get the Laplace Transform of, and Sketch the complex...

Homework Statement Solve df/dx (x)+ f(x)= 3 under the condition f(0)= -2 using the Laplace transformations Homework Equations The Attempt at a Solution Not even sure where to start on this one. Dont have any examples that point me in the right direction. Any ideas anyone??

Homework Statement y(x) = e^{3x} + \int_0^{x}\hspace{1mm}y(t)\hspace{1mm}e^{x-t}\hspace{1mm}dt Homework Equations (f*g)(x) = \int_0^{x}\hspace{1mm}y(t)\hspace{1mm}g(x-t)\hspace{1mm}dt L(f*g;s) = L(f;s)L(g;s) I will use Y(s) to denote L(y;s) The Attempt at a Solution I tried...

I read through that 800 something page Dover book on differential equations, but I feel like I haven't had enough practice. I need several problems and solutions, but mostly Laplace transform problems. In fact even just Laplace transform problems would be greatly appreciated.

After solving a simple circuit with a inductor L in series with resistor R Driven by Voltage source V0 by using Laplace Transform we get I(s) = \frac{V}{s (R + Ls} Why do we call this the frequency Domain response? What does 's' represents?

Laplace Transform of... Few months back my friend called me to help him (and his whole class!) finding the Laplace Transform of \sin \sqrt{t}. Since then I found myself wasting hours and days (even before non-mathematics exams!) trying to solve the problem. I also checked the provided answer...

Homework Statement \mathcal{L}\left[\frac{\sin(t)}{t}\right]=? Homework Equations \mathcal{L}\left[f(t)\right]=\int_0^\infty e^{-zt}f(t)dt The Attempt at a Solution \int_0^\infty e^{-zt}\frac{\sin(t)}{t}dt=\int_0^\infty \frac{e^{-zt}}{t}\left(\frac{e^{it}-e^{-it}}{2i}\right )dt...

F(s) = \frac{1}{K^s} where K is a positive real.

Homework Statement solve the differential equation by using Laplace transform x^{''}(t)+7x^{'}(t)+10x(t)=sin3t x(0)=0, x^{'}(0)=0 Homework Equations X(s)s^2+X(s)7s+X(s)10=\frac{3}{s^2+9} then i get X(s) = \frac{3}{s^2+9}\cdot\frac{1}{(s+5)(s+2)}...

Homework Statement Find the Laplace transform of the given function, a and b are real constants. Hint: cos(bt)=(e^ibt+e^-ibt)/2 and sin(bt)=(e^it-e^ibt)/2i. f(t)=e^(at)*sin(bt) The attempt at a solution The LaPlace transform of e^at is 1/(s-a). The LaPlace transform of sin(bt) is...

Hi all Conventionally we used to seeing the Laplace transform applied to problems that use time as the independent variable, can anybody point me at some examples that do not use time as the independent variable? Thanks Tim

Homework Statement I'm trying to solve a definite Laplace transform. The function is defined as f(t) = sin(t) over the interval [0, \pi] Homework Equations The integrate to evaluate is: \int_0^\pi e^{-st} sin(t) dt The Attempt at a Solution To evaluate, first use integration by...

Homework Statement So I finally had my final today, and I was so worried because I needed a 90% at least to pass the class with an A. :\ So I'm really worried with a few of my answers. One of those (that I can remember) was the laplace transform of: t(sinh(3t). Homework Equations laplace t...

Homework Statement 2y'' + y' + 4y = ∂(t-π/6)sin(t); y(0)=0, y'(0)=1/2. Homework Equations Dunno The Attempt at a Solution The left side of the equation is what's tripping me up. There's nothing on my Elementary Laplace Transforms table that has the Dirac delta function...

Hello, I am trying to find the laplace transform of \frac{f(t)}{t} http://nptel.iitm.ac.in/courses/Webcourse-contents/IIT-KANPUR/mathematics-2/node92.html Lemma 10.3.9 I don't understand why we are taking the limit as s goes to infinity Can anyone help me? thank you

Just out of curiosity, I've been looking into the Laplace transform and noticed that... \mathcal{L}(sin(t))=\frac{1}{s^2+1}=\frac{d}{ds}(tan^{-1}(s)) So, I was wondering if the Laplace transform of the sinc function was the inverse tangent function. In LaTEX...

Homework Statement http://img710.imageshack.us/img710/3381/38442384.jpg The Attempt at a Solution [PLAIN][PLAIN]http://img695.imageshack.us/img695/6295/56987528.jpg Thanks in advance, JJ

Find the laplace transform {\cal L} (1 + t) Without using the table. im really having a hard time working these out please help!

Compute L[(t-3)u2(t) - (t-2)u3(t)] I come up with using unit step function but I don't know how to solve it

one of the questions my diff eq teacher gave us is L{(t^3)(sin^3(t))} (laplace of t cubed sine cubed t) i'll just cut to the chase and ask, would you be of the opinion that a question like this is in the scope of an intro to ODE class?

Homework Statement Solve using the Laplace Transforms (can not use partial fractions) f '(t) + \int2f(u) du = 2 + 3f(t) Homework Equations Using Laplace f '(t) gets replaced with sF(s) -f(0) \int2f(u) du gets replaced with \frac{2F(s)}{s} Please correct me if I'm wrong on...

Homework Statement \frac{s}{(s-a)(s-b)} Homework Equations Now I know that it results in: [tex]\frac{ae^(at)-be^(bt)}{a-b}[\tex] The Attempt at a Solution OK, I don't have the slightest clue where to begin. Could someone point me in the right direction? I've looked at all...

Homework Statement Let f(t) denote a causal signal. Show that L+ {f(−at)} = 0 for any a > 0. Homework Equations The Attempt at a Solution I know that the laplace{f(at)} = 1/a*F(s/a) but by simply placing -a whenever determining the Laplace, my signs gets confused within the...

Homework Statement Find the unit impulse response for the operator D^4 + I, using the Laplace transform. Homework Equations The Attempt at a Solution w^(4) + w = δ(t) s^4W + W = 1 W = 1 / (s^4 +1) Now, I need to find the inverse laplace transform of W. But I don't know how to simplify W...

Homework Statement It's been a while since I've done laplace transforms, but I need some help with one! I am supposed to find the laplace tranform for the following signal. This is for my circuits class btw. xa(t) = 2u(t-1) Homework Equations Laplace tables...

Homework Statement Using laplace transform, solve: y'' - y = \frac{x^2-3x+2}{|x^2-3x+2|} y(0)=y'(0)=0 Homework Equations The Attempt at a Solution Just to know if I'm on the right path - Since the quadratic has 2 roots, at 1 and at 2, the entire thing can be equal to...

Homework Statement Not a homework problem exactly, but in an EE textbook I saw something to the following effect: To obtain the time domain behavior for \frac{s}{s^2+\frac{\omega_0}{Q} + {\omega_0}^2} the following Laplace transforms are combined to cancel the term in the numerator...

Homework Statement Need to find the Laplace transform of |sint| (modulus). Homework Equations The Attempt at a Solution I am really not sure how to proceed here - any help would be much appreciated.

Homework Statement I need to find the inverse Laplace transform of s/(s^2+a^2), where a is a constant, by the method of residues. I need to prove the part of the contour not actually relating to the desired integral tends to zero as R---> infinity. Homework Equations The...

Hello PF, maybe you can help with this one! I need to show that the Laplace transform of J0(at) is (s^2 + a^2)^-1/2. My prof told me to start with the form: x2y'' + x y' + (x2 + p2)y = 0, where p = 0 ITC. What have I got so far?... Doing the Laplace transform on both sides, where Y...

Homework Statement Calculate the inverse Laplace transform of exp(-as)/s (a is a constant). Homework Equations The Attempt at a Solution I need to calculate the integral (1/2*pi*i)int(c-i(inf), c+i(inf))(exp(s(t-a))/s). I'm guessing I need to integrate around a circular...

How can I solve this Laplace transform (or how can I find series solution)? http://www.forkosh.dreamhost.com/mathtex.cgi?M=\int[/URL] _0^{\infty }e^{-\text{kR}}J_1^2(\text{ka})dk[/PLAIN] ;R>2a

Homework Statement ...find the inverse transform of the given function. F(s)= (2s+2)/(s2+4s+5) Homework Equations On another page, I see these 2: f(t)=eatsin(bt)--------->F(s)=b/[(s-a)2+b2) f(t)=eatcos(bt)--------->F(s)=(s-a)/[(s-a)2+b2) The Attempt at a Solution This is my first time...

Homework Statement y'' -6y' + 9y = f(t) f(t)= 0, 0<t<1 1, 1<t<3 0, t>3 Homework Equations The Attempt at a Solution Turning it to heaviside functions I get: y'' -6y' + 9y = u1 - u3 and I solve. in the answers it should be: y(t) = 2tet + u1(1/9 - 1/9e3(t-1)+...

Laplace Transform of unit step function HELP! Homework Statement f(t)= e^t on 0<=t<1 . . . . t on 1<=t<2 . . . . sin(t) on 2<=t<infinity Homework Equations Unit Step Function The Attempt at a Solution Here is my attempt at a solution...

I'm trying to use the Laplace transform to work out another capacitor problem, the voltage as a function of time on a capacitor that's discharging into another capacitor through a resistor. It's the classic two capacitor problem, but I'd like to actually find an expression for the voltage as a...

Homework Statement I'm trying to use the Laplace transform to find the charging equation of a capacitor with an initial voltage already on the capacitor.Homework Equations V_i = RC\frac{dVc}{dt} + V_c The initial condition of Vc will be \lambda. The Attempt at a Solution V_i(s) = sRC*V_c(s)...

Homework Statement Given: \frac{d^2y}{dt^2} + 12\frac{dy}{dt} + 32y = 32u(t) and that all initial conditions are zero, use the Laplace transform to find y(t) This is an example problem from my text. They start the solution by taking the Laplace of both sides assuing y'(0) = 0 & y(0)...

Homework Statement t y'' + (3 t-1) y' + 3 y = 6 e^{-3t} y(0) = 1 y(5) = 2 Homework Equations The Attempt at a Solution I tried applying the Laplace transform to the equation but I was having a little trouble... L [t·y''] = -dL[y'']/ds = s2·Y' + 2·s·Y - y(0) = s2·Y' + 2·s·Y - 1 L...

I am asked to find inverse laplace of (3s+5)/(s^2-6s+25) I do partial frac and get (3s)/((s-3)^2+16) + (5/(s-3)^2+16) I do the translation and get [(3s)/s^2+16 + 5/(s^2+16)]*e^3t My final answer is e^3t[3cos(4t) + 5/4sin(4t)] but the book says the sin term should be 7/2sin(4t)? I say...

Homework Statement Could \[F(s) = \frac{1}{{s(1 - {e^{ - s}})}}\] be the Laplace transform of some periodic function? Why? If so, find that periodic function The Attempt at a Solution If it was the Laplace transform of some periodic function, the the Laplace transform of the first wave...

Homework Statement If f(t) transforms into F(s), so that \[ F(s) = \frac{{s + 1}}{{s^2 + as + 1}},a \in \] , prove that if a < 0, the function f(t) isn't bounded, and if a >= 0, it is bounded. Prove that if -2 < a < 2, f(t) oscilates. The Attempt at a Solution I honestly have...

I have this DE: \[y'' - 4y' + 8y = f(t) = \left\{ \begin{array}{l} t{\rm{ }},t \in [0,2) \\ t + 1{\rm{ }},t \in [2,4) \\ 0{\rm{ }},t \ge 4 \\ \end{array} \right.\] I have problems transforming f(t). I know that when I have a function defined by parts, I...

Hello, I am trying to take the Laplace transform of floor(f(t)) in order to solve the differential equation f'(t)=floor(f(t)). I know that http://functions.wolfram.com/IntegerFunctions/Floor/22/04/" gives L(floor(t)) = (e^(-s))/(s(1-e^(-s))) instead -- are these equivalent?) and L(f(t)) =...

Hello, I am trying to take the Laplace transform of floor(f(t)) in order to solve the differential equation f'=floor(f(t)). I know that L(floor(t)) = (e^(-s))/(s(1-e^(-s))) and that L(f(t)) = F(t) (of course), but I realized that I have no idea how to take the Laplace transform of a...