Laplace Definition and 1000 Threads

Here is the question: Here is a link to the question: Consider the initial value problem for y; Laplace? - Yahoo! Answers I have posted a link there to this topic so the OP can find my response.

While reading Laplace transform in my book, I came across a problem. where it evaluates the laplace transform of f(t)=1/√t => √(π/s) . But is the laplace transform of f(t) really exists? because I thought the function f(t) is not defined at t=0 and it tends to infinite. So How is it...

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...

Homework Statement ODE: y'' + 4y' + 3y = f(t) f(t) = (?? HELP - What's the mathematical term to describe these? I can't seem t o find it in my notes :cry: ) 1, 0 ≤ t < 2 t², 2 ≤ t < 3 0, t ≥ 3 Write a brief description on how you would solve this ODE using Laplace transforms. Also use the...

Homework Statement Differential equation: \frac{d^2x}{dt^2}+4\frac{dx}{dt}+4x=6e^{-2t} with initial conditions x(0)=-2 and \frac{dx}{dt}(0)=8 Use the laplace transform to solve for x(t) Homework Equations http://www.atp.ruhr-uni-bochum.de/rt1/syscontrol/node9.html...

Homework Statement A system is characterized by the equation y' + 3y = r' . When the input is r(t) = u(t) - u(t-1), find y(t) by taking the inverse Laplace transform of Y(s).Homework Equations The Laplace transform integral The Laplace transform of a derivative sF(s) - f(0) The transfer...

Homework Statement Shown in attachment Homework Equations The Attempt at a Solution I'm trying to analyze the circuit in the attached picture. This is a step response with a 3V input or 3u(t). What I've done so far is: 1. convert all of the components to the s-domain. R = R, L = sL, C =...

Hi I was wondering what the Laplace transform of a squared differential is. With that I mean the Laplace of (y' )^2 (this being y'*y' and not the second order derivative). So for example velocity squared.

Homework Statement Homework Equations The Attempt at a Solution The answer is y(t) = t^{4}+\frac{t^{6}}{30} Don't know what to do next any advices please

*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...

Homework Statement Find the Laplace transform of the following function t[SUP]2[SUP] - 2t The Attempt at a Solution \[\begin{gathered} f\left( t \right) = {t^2} - 2t \hfill \\ l\left( {f\left( t \right)} \right) = F\left( s \right) = \int_0^\infty {{e^{ - st}} \cdot \left( {{t^2} - 2t}...

Using Laplace can someone please show me in simple terms how i would solve the following function? This is a lecture example. The solution just shows the answer, nothing about how we get it or what it represents. I am finding this subject particularly difficult to come to grips with. δ(t-1)...

Homework Statement I'm stuck on finding the inverse of this circuit. Can anyone please check my work, In this circuit you are suppose to find v(t) when switch moves to point 2 ( meaning deattached from battery). Homework Equations The Attempt at a Solution...

This is very tricky for me. How to find the inverse laplace of 1s. I haven't been taught the integral method of inverse. Only the formula based , splitting terms kind of thing. I used MATLAB and found it was dirac delta. But how do I get to it without using the integral for inverse?

Homework Statement f(t) = cos (pi*t) if 1\leq t <4 and 0 elsewhere using unit step functions to find Laplace TransformHomework Equations The Attempt at a Solution I came up with the unit step function f(t) = cos(pi*t) u(t-1) - cos(pi*t) u(t-4) in order to use the second shifting theorem f(t)...

Homework Statement So I have this laplace transformation chart and was a bit unsure about the laplace and inverse laplace of this. The unit step function, where u(t) = 0 where t < 0, u(t) = 1 where t > 0. The laplace transformation chart that I have has two columns, the column on the...

Homework Statement find the inverse laplace transformation of \frac{5s+4}{s^2} e^{-2s} Homework EquationsThe Attempt at a Solution I have tried to partial fractions \frac{5s+4}{s^2} and I got \frac{5}{s}+\frac{4}{s^2} and I know that the answer must have u(t-2) because of second shifting (...

Homework Statement Could anyone please check my work, The answer is wrong. Correct Answer: e^2t(-t+e^t-1) Homework Equations Inverse Laplace The Attempt at a Solution Here's my solution, please point out my mistakes. One mistake i found after taking the picture is: Its -2te^-2t ( third...

Homework Statement see attachment Homework Equations The Attempt at a Solution I don't get the part where it says "Solving this equation for X(s), we obtain ..." Specifically jumping from 3/s(s2+3s+5) to (3/5)(1/s)-(3/5)[(s+2)/(s2+2s+5)]. How did the problem break up this...

Hello! Do somebody know where the code for calculating a determinant by Laplace theorem (in Fortran) can be found? Or maybe somebody could help with this issue. Thank you!

I am doing a laplace transform as part of a coursework assignment. I have some example transpositions that are relevant to the question I am answering but I can't see how the author has got from one arrangement to the next. [b]2. Homework Equations He has given 1/(s^2(τs+1)) =...

I'm applying laplace transform to a spring-mass system, the most basic one. I write this code which takes initial values x(0) and v(0) as input and I'm computing x(t) in matlab. But for some values it gives me complex roots for x(t) which doesn't seem possible. If not for laplace I can solve the...

I have a question asking for the inverse laplace transform of (e^(-s))/(s^2+pi^2). I split it up to (e^(-s))/s x s/(s^2+pi^2) and got u(t-1)cos(pi(t-1)),but the correct answer is (sin(pi(t-1)/pi)u(t-1). So here it was split up to (e^(-s))/pi x pi/(s^2+pi^2) and I don't understand where the...

The following diff. equation describes the functionality of a system with respect to time. However, it is not known how the system will behave when stimulated. Apply a forward Laplace transform to determine damping ratio and pole zeros. Plot a pole zero diagram and comment on stability. d2y/dt2...

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 What is the inverse laplace transform of (1/(s+s^3))? Homework Equations The Attempt at a Solution I looked it up on wolframalpha and got 1-cos(t), but I don't understand how they got that answer. I looked up a basic laplace transform chart and didn't see anything...

Homework Statement General solution for eccentric spheres, smaller sphere (radius, b) completely embedded within larger sphere of radius c. The centers of both spheres lie on z-axis, distance a, apart (note: c>b+a). Problem is symmetric, so consider θ=[0,∏], r=[0,c]. The inner sphere is...

The length of the side of the square is a. The boundary conditions are the following: (1) the left edge is kept at temperature T=C2 (2) the bottom edge is kept at temperature T=C1 (3) the top and right edges are perfectly insulated, that is \dfrac{\partial T}{\partial x}=0,\dfrac{\partial...

Homework Statement Find inverse Laplace transform \mathcal {L}^{-1}[\frac{1}{(s^2+a^2)^2}]Homework Equations The Attempt at a Solution I try with theorem \mathcal{L}[f(t)*g(t)]=F(s)G(s) So this is some multiple of \mathcal{L}[\sin at*\sin at] So \mathcal {L}^{-1}[\frac{1}{(s^2+a^2)^2}]=\propto...

Hello, I am trying to figure out in my notes how my professor did L[(e^-3t)(sin2t)] = 2/(s+3)^2 +4 I think she just did it in her head and wrote it, so I don't actually know how to solve it. I am looking at my table of laplace transforms and there is none for a product of an exponential and...

Homework Statement y''-4y'-32y={1 when 0<=t<1 and 0 when 1<=t y(0)=y'(0)=0 Homework Equations The Attempt at a Solution s2L(y) -4sL(y)-32 L(y)=u1(t) I am just struggling to figure out if my unit step function is correct. Solving for L(y) I get: (e-s) / (s(s2 -4s-32))...

I'm having trouble with this question. Can anyone please guide me. My Attempt : = 1/(s-1) * L{t^2*e^-t} = 1/(s-1) * (2/(s+1)^3) = 2/((s-1)(s+1)^3)) but that's not the answer , its 2/((s-1) s^3) somehow. The question is attached below.

Homework Statement Find the inverse laplace transform of (2/(s+2)^4) using the given table of identities: Homework Equations Here are the given identities: The Attempt at a Solution Alright, I realize that there is a simple identity that I can use with a factorial symbol, but this...

I thought it would be obvious, but I can't find a series representation of the Laplace transform. I'm looking for something analogous to the Fourier series and how it can be used to derive the Fourier transform. I though it would simply be f(x) = \sum_{s=-\infty}^{\infty}{C_{s} e^{sx}} , but...

This is a conceptual question on the region of convergence (ROC) and the inverse Laplace transform (ILT). Here the bilateral laplace transform (LT) and the ILT are given by F(s)=L\{f(t)\}=\int_{-\infty}^{+\infty} f(t) e^{-st} dt and f(t)=L^{-1}\{F(s)\}=\frac{1}{i...

why was laplace transform developed i have googled it and found that it is something about shaping a family of exponential and vector projections etc i couldn't get it. some simply said that it was used to make a linear differential equation to algebraic equation but i couldn't understand how...

Homework Statement L[t^{2} - t^{2}δ(t-1)] Homework Equations L[ t^{n}f(t)] = (-1^{n}) \frac{d^{n}}{ds^{n}} L[f(t)] L[δ-t] = e^-ts The Attempt at a Solution My teacher wrote \frac{2}{s^{3}} -e^{s} as the answer. I got \frac{2}{s^{3}} + \frac{e^-s}{s} + 2 \frac{e^-s}{s^2} + \frac{2e^-s}{s^3}

Homework Statement Use Laplace transform to the system: \frac{dy}{dt} + 6y = \frac{dx}{dt}3x - \frac{dx}{dt} = 2\frac{dy}{dt} x(0) = 2 ; y(0) = 3 The Attempt at a Solution I've tried everything on this one. I first solved \frac{dy}{dt} + 6y = 2\frac{dy}{dt} and I got y = 3e^{6t} ...

Homework Statement Problem 8-19 in Matthews and Walker's book on mathematical physics. A straight wire of radius a is immersed in an infinite volume of liquid. Initially the wire and the liquid have temperature T=0. At time t=0, the wire is suddenly raised to temperature ##T_0## and...

Homework Statement this one stumped me.. d^2y/dt^2 +ωy=ksin((√ω)t) y(∏/4)=0, y'(∏/4)=0 The Attempt at a Solution → (s^2 + ω)U(s)= LT {ksin((√ω)(T+∏/4)} is as far as i can get (i know what to do with the left hand side once i get the LT of the right hand side but i don't know what to do with...

Homework Statement Heat equation in a annulus, steady state solution. u(a,θ,t) = Ta u(b,θ,t) = Tbcos(θ) Homework Equations Using separation of Variables \frac{}{}\frac{1}{r}\frac{d}{d r}(r\frac{d R}{d r}) + \frac{1}{r^2}\frac{d^2\Theta}{d \theta} = 0 The Attempt at a Solution...

Why is it that the unilateral lateral Laplace transform is used when given initial conditions that are non-zero. Is there a reason that explains why it would be wrong to use the bilateral Laplace transform instead? I know bilateral does not have any input of initial conditions but that does not...

How we get relation \lim_{t\to 0}f(t)=\lim_{p\to \infty}pF(p)? Where ##\mathcal{L}\{f\}=F##.

Homework Statement Evaluate the Laplace transform: L{δ(t-∏)tan(t)} Homework Equations The Attempt at a Solution L{δ(t-∏)tan(t)} = ∫ δ(t-∏)tan(t) dt evaluated from 0 to ∞ =tan(∏)e-∏*s = 0 Could someone check my work on this one? I'm suspicious that my transform is just zero...

Homework Statement y" + y = 4δ(t-2π); y(0)=1, y'(0)=0 Homework Equations L[f(t-a) U(t-a)] = e^{-as} L[f(t)] L[δ(t-c)] = e^{-cs} The Attempt at a Solution My answer is: cos(t) + 4U(t-2π)sin(t-2π). When I used Wolframalpha it gave me 4sin(t)U(t-2π) + cos(t)

Homework Statement L[cos2at] I know that L[cost] = s/(s2+bs) I know that cos2at can also be written as 1/2(1+cos2at) and so I then got the L[1/2]+1/2L[cos2at)] Which gave me s/(s2+(2a)2) However this is not correct, there was a + 2at term on the numerator as well. Homework...

Hello if our function is how it convert to ?

Homework Statement Homework Equations I really wish they existed in my notes! *cry*. All I can think of is that integrating or in other words summing the dirac delta functions for all t, would be infinite? None the less the laplace transform exist since its asked for in the question and i...

Homework Statement Homework Equations Assume the solution has a form of: The Attempt at a Solution It looks like a sine Fourier series except for the 2c5 term outside of the series, so I'm not sure how to go about solving for the coefficients c5 and c10. Any idea?