Laplace transform Definition and 752 Threads

Homework Statement Please help by explaining in detail how to find the Laplace transform of the function f(t) = { 2 0 <= t < 3 { -2 t >= 3. Homework Equations The Attempt at a Solution For the most part I know that U(t-3)(t-3). I want to account for the amplitude...

I hope somebody's up tonight, this is due in the morning and I'm so close. So I was assigned to solve this differential equation using laplace transforms and although I (think I) can solve it, I'm not getting the same answer that Maple spits out. The DE is: x'' + 2x' + 5x =...

Homework Statement This has to do with the unit step function. The question is; Sketch the function g(t) = 1 for 0<t<1 and is 0 for t>1. Express g(t) in terms of the unit step function and hence or otherwise show that L(g(t)) = 1/s^2 - e^-s (1/s^2 + 1/2) Homework Equations...

[SOLVED] Laplace Transform Homework Statement Suppose F(s) = \displaystyle\mathcal{L}(f(t)) Show that \displaystyle\mathcal{L}(f(ct)) = 1/c F(s/c) Homework Equations The Attempt at a Solution \displaystyle\mathcal{L}(f(t)) = \int_0^{inf} e^{-st} f(t) dt \displaystyle\mathcal{L}(f(ct)) =...

[SOLVED] Laplace transform Homework Statement Find the inverse laplace transform of \frac{e^{-2s} }{s^2 + s - 2} Homework Equations The Attempt at a Solution I'm able to do about half of the problem using partial fractions, I've found...

let be a function f(t) , and i want to prove that f(t)=O(t) in big-O notation. i know that Laplace transform of f(t) is F(s) then i perform the integral F(s)= \int_{0}^{\infty} dt f(t) e^{-st} if we assume f(t)=O(t) then F(s)= \int_{0}^{\infty} dt f(t) e^{-st} \le \int_{0}^{\infty}...

Homework Statement determine the inverse laplace transform f(t) of the function Homework Equations F(s) = 3/s - (4e^-s)/s^2 + (5e^-2s)/s^2 The Attempt at a Solution i broke it up into the 3 part and got them seperatly which gave me f(t) = 3 - 4u(t-1)(t-1) + 5u(t-2)(t-2)...

My goodness.. I have not come across an inverse Laplace transform like this. My teacher let's us just use a chart to figure them out, but this is definitely not on there. How do I find the inverse Laplace transform of: { (1/2)+[(5e^-6s)/(4s^2)] } / (s+5) I already used partial fractions to...

I am trying to find the Laplace Transform of a chirp: Essentially this requires evaluating an integral between zero and infinity of: (exp(s*t))*sin(t^2) with respect to t where s is the parameter (Laplace space frequency). Any help or advice or a redirect to some useful link would be much...

[SOLVED] Laplace transform, book example I'm having trouble following one of the steps in my textbook. They give a function: y(t) = e^{2t} and plug it into Y(s) = \int_{0}^{\infty} y(t) e^{-st} dt and compute. They end up with: \frac{1}{2-s} \underbrace{lim}_{b -> \infty} e^{(2-s)b}...

iv got a problem i can't seem to understand. if anyone could help me out it would be great f(t)= sin2tcos2t im just not sure what to do when i have the product of 2 trig functions. the correct answer is (2/(s^2 + 16)) thanks for any help

[SOLVED] Laplace Transform question Homework Statement Use the Laplace transform to solve the given IVp {\frac {d^{2}}{d{t}^{2}}}y \left( t \right) +2\,{\frac {d}{dt}}y \left( t \right) +5\,y \left( t \right) ={e^{-t}}\sin \left( 2\,t \right) y(0)=1, y'(0)=-1Homework Equations L(f) =...

[SOLVED] Laplace Transform (Should be easy) Homework Statement I know there are other ways to solve this, but I HAVE to use Laplace Transformy''-y'-6y=0 where y(0)=2 and y'(0)=-1The Attempt at a Solution Written as Laplace: y''-y'-6y=0 \Rightarrow...

Hey everyone Does anyone know how to do the following Laplace Transformation f(t) = e^t *sin(t)sin(5t) i can do it with one sin function but don't know how to do it with 2. any help would be appreciated.

Homework Statement Inverse Laplace Transform of given, F(s) = s/((s^2)+2s+10) Homework Equations n/a The Attempt at a Solution I reduced it down to s/(((s+1)^2)+9) but I can't find the proper form of it, meaning I have to reduce is a little bit more but I can't think of a way to...

Homework Statement Determine L{t sinwt} with the aid of therom 1.31 (its the General Differentiation method on this page: [PLAIN]"link"[/URL] Homework Equations Shown on linked page The Attempt at a Solution I do not understand how to start this becasue I do not have a...

Homework Statement Laplace transform from f(x) = x cos(ax) to ^f(s) = (s^2 - a^2) / (s^2 + a^2)^2 how do you get the -a^2 term in the numerator, all i come up with is s^2? Homework Equations f(x) = x e^(ax) ----> ^f(s) = 1/(s-a)^2 2 cos(ax) = e^(aix) + e^(-aix) The Attempt...

I'm looking some applied example of Laplace transform. For instance: If I have function f(t) = Asin(ωt + φ), where; A is peak deviation from center ω is Angular velocity t is time φ is phase and now I want to laplace transform it and get some function like...

1. Find v(t) if V(s)=\frac{2s}{(s^{2}+4)^{2}} Ans: v(t)=\frac{1}{2}tsin2tu(t) 2. Homework Equations : V(s)=\frac{a_{n}}{(s-p)^{n}}+\frac{a_{n-1}}{(s-p)^{n-1}}+\cdots+\frac{a_{1}}{(s-p)} a_{n-k}=\frac{1}{k!}\frac{d^{k}}{ds^{k}}[(s-p)^{n}V(s)]_{s=p} 3. Attempt at a solution...

My textbook provides a proof but there's one thing about the proof i do not understand it starts assuming L{f(t)} = the laplace integral with the f(t) changed to f(a) same goes with L{g(t)} as it changes it to g(b) i understand the big picture>>starting from a product of 2 L transforms...

Given... (2s^{2}+1)e^{-s} ------------------ (s - 1)(s^{2} + 4s + 5) Find the inverse Laplace Transform. I am unsure where to start and am just looking for a little direction, not an answer. From past experience, I am assuming I will have to rewrite this in another form...perhaps by...

Laplace transform... I can't help but keep asserting how me textbook of differential equations just keeps stating new ideas without any background on WHY and HOW they were created. I've just started Laplace transform and the first thing i see is a blue DEFINITION box that just states the...

Hello, I have a fairly straight forward question regarding an inverse laplace transform. The function follows along with the solution. The solution (provided in my text) has been confirmed by Maple; however, i cannot account for the (1/3) in the solution. Any help would be greatly...

Homework Statement Find the Laplace Transform of the following: 5{\delta (t-3)}+4{u(t-2)}+3{e^{-5(t-3)}u(t-4)} The Attempt at a Solution I know how to do the first and second terms, but I'm having trouble with the third. 5e^{-3t}+4\frac{1}{s}e^{-2t} + ? I think I should be using...

So I know the laplace transform of an integral is the product of the laplace transorm of the functions inside the integral, such as Laplace{integral from 0 to t [tau*e^(t - tau) d tau = Laplace[t] * Laplace[e^t], ignoring the tau what if I have Laplace{integral from 0 to t [t*e^(-tau) d tau]...

what's the answer for laplace transform of the questions below? 1. cos(4t-1)u(t-1) 2. cos4(t-1)u(t-1) I want to compare the difference between these two answer. Thanks!

Homework Statement Find the Laplace transform of the following functions f(t)= sine squared t Homework Equations sin kt = k^2/(s^2 + k^2) The Attempt at a Solution I went like this; sin squared t is sin t* sin t therefore it should be 1/(s^2 +1) (s^2 + 1) but...

Homework Statement I must find the solution of a differential equation, but I'm stuck with a problem of algebra; Homework Equations The problem is y''+2y'+2y = sin(at) With y(0) = y(0)' = 0 y''+2y'+2y = sin(at) s^2L[y]+2sL[y]+2L[y] = \frac{a}{s^2+a^2} L[y](s^2+2s+2) =...

Homework Statement What is the Laplace transform of f(t) = t^2 - 18 for 0 < t < 3 and f(t) = (t-3)^2 for t>3?Homework Equations Laplace Transforms 3. Work Using Heaviside/step function, made equation into: f(t) = t^2 - 18 + u(t-3)( (t-3)^2 - (t^2-18) ) Then, using Laplace transforms...

PDE is type of heat equation. Many book only gives an example of solving heat equation using Fourier transform. An exercise asks me to solve it for using Fourier and laplace transform: In the heat equation, we'd take the Fourier transform with respect to x for each term in the equation...

Homework Statement Use Laplace Transforms to solve the following initial value problems a. t\,y''\, - \,t\,y'\, + \,y\; = \;2\;\;\;y(0)\;=\;2\;\;\;y'(0)\;=\;-1 b. y''\,+\,2\,y'\,-3\,y\;=\;\delta(t\,-\,1)\,-\,\delta(t\,-\,2)\;\;\;y(0)\;=\;2\;\;\;y'(0)\;=\;-2 Homework Equations Laplace...

I couldn't figure the sol'n for this problem Could somebody help? Thanks a lot Find the following Inverse Laplace transform (L^(-1))*[1/(4s+1)]:frown:

Homework Statement Suppose f(t) is a periodic function with period T. Show that the Laplace transform of f is: L(f) = \frac{1}{1-e^{-sT}}\int_0^T f(t)e^{-st} dtThe Attempt at a Solution I started with the definition of a Laplace Transform for f: L(f) = \int_0^\infty f(t)e^{-st}dt Using the...

Homework Statement Solve the initial value problem: \frac{dy}{dt} + 2y = u_2(t)e^{-t} y(0) = 3 Where u_2(t) is a Heaviside Function with the discontinuity at t=2. Homework Equations The Laplace transform of a Heaviside function multiplied by another function: L( u_a(t)f((t-a) ) =...

Hi all, Just a small question: I came across a problem to solve a differential equation using Laplace transform. I solved the major part but only still a part where I had to inverse transform the following experssion: (exp(-s))/(s^2) I looked in Laplace Transform Tables but did not...

Gents, I have this problem: find the inverse laplace transfor for Y1(s) = exp(-s)/s^2 Y2(s) = {1/[4*(s+1)]}*exp(-2*s) my solution is: using the 2nd shifting theroem y1(t) = (t-1) H(t-1) y2(t) = (1/4)*exp(2-t)*H(t-2) Is my solution correct?

Need urgent help on laplace transform and PDE ! I'm stuck with this 2 questions ... q1) Using laplace transforms, solve: y" + 4y = r(t), where r(t) = {3sint, 0<t<pi, -3sint, t>pi y(0)=0, y'(0)=3.[/color] this is what i get after rewriting for the step function: 3sint [1-u(t-pi)] +...

I am trying to find the inverse LaPlace transform of F(s)=\frac{2s+12}{s^2+6s+2\sqrt{2}} Using partial fraction decomposition on the above rational expression seems tedious. Is there any other method? Thanks

Homework Statement Using convolution theorem for Laplace theorem,, show that Homework Equations inverse Laplace transform (1/(S^3/2*(s-1)) = (2*e^t)/Pi^1/2 intregral (from 0 to t) e^-x*x^1/2dx. The Attempt at a Solution The inverse Laplace above is a product of 1/s^3/2 and...

[b]1. The zero order bessel function J0(0+) = 1, J'0(0+) = 0. and J0(t) satisfies teh differential equation [b]2. ty''(t) + y'(t) + ty(t) = 0, t>0 Prove thata the Laplace transform of J0(t) is 1/(s + 1)^1/2 The Attempt at a Solution Could anyone help on this. How to I go about with...

I am trying to show that L[t^m] = m!/s^m+1, unfortunately I can not understand why integral from 0 to inf of (t^m)(e^-st)dt = (-d/ds)^m. integral 0 to inf of e^-stdt... ?

\int_{0}^{\infty} x dx = \left[ \frac{1}{2}x^2 \right]_{0}^{1} = \frac{1}{2}

My book on signal processing says that: f(t) = \frac{1}{2\pi j} \int_{c-j\infty}^{c+j\infty} F(s) e^{st} ds = \lim_{\Delta s \to 0} \sum_{n = -\infty}^{\infty} \Big[ \frac{F(n\Delta s)\Delta s}{2\pi j} \Big] e^{n\Delta s t} I don't get this. How/Why can you write a integration over a...

Hi every body, I am not so sure this kind of question is suitable here. In styding maths, I have some difficulties with the Laplace transform. The formulas are OK, I can apply them, but I still do not understand the physics meaning behind that. Can anyone can explain to me a little bit more...

how do i go about solving the laplace transform of sint * cost ? i know the answer becomes 1/(s^2 + 4) but what is the method? thanks.

Homework Statement solve the following initial value problem using Laplace transforms y"+2y'+y=(8/3)cos(2t)-2sin(2t) y(0)=1 y'(0)=7/3 Homework Equations L[d^2y/dt^2]=s^2Y-sy(0)-y'(0) L[dy/dt]=sY-y(0) L[coswt]=s/(s^2+w^2) L[sinwt]=w/(s^2+w^2) The Attempt at a Solution so...

Homework Statement 1/s^5 Homework Equations I was thinking I need to use n!/s^n+1 The Attempt at a Solution But n would then be 4, so n! will be 24. Not sure what to do?

Can we use laplace transform to solve an ODE with variable coefficients? Like this one: 4x y" + 2 y' + y = exp (-x)

Hi everyone, I need to solve this ODE using the laplace transform: y" + y - exp (-t^2) = 0 , y(0) = y'(0) = 0 My question is on how to find the laplace transform of exp (-t^2). I used different properties of laplace transform to solve it but I was not succesfull. I was thinking that I...

Can someone tell me if I did this right because my solution seems wrong, but I've done it a couple times and get the same answer. I'm given the following: x' + 2y' + x = 0 x' - y' + y = 1 and the initial values of x(0) = 0 and y(0) = 1 The idea is to solve this initial value problem. Can...