Laplace Definition and 1000 Threads

Dear All, When I have a equation 1/sT its an integrator with time constant i.e Assuming a T of 5s, if I input a unit step function, the output of the integrator reaches unity in 5 seconds atleast I undestand it that way. Please correct me if I am wrong in the same way can someone help...

Hi, I recently posted another question about a Laplace transform and now have a question about taking the inverse Laplace transform. Again, my professor did not cover this topic as well as I could have hoped for, and so I am stuck on this problem as well. Again, I understand the idea of Laplace...

Hi, I've been asked to find the Laplace transform of a function and I have not the slightest clue where to begin. My professor derived the basic Laplace transforms in class(sin, cos, delta function, step function, etc), all of which I understood perfectly. However, he never really gave us an...

We use this plane called the "Laplace plane" to solve problem in control-engineering, second order systems. Can anyone help explain the Laplace plane in simple words? I find the wiki article too fancy for me... it says that it "is a mean or reference plane about whose axis the instantaneous...

Homework Statement y'' + w^2y = cos(t) y(0) = 1 y'(0) = 0 w^2 not equal to 4 Homework Equations Laplace integral, transform via table/memory... Y(s) = F(s) or whatever you like to use The Attempt at a Solution s^2Y(s) - sy(0) - y'(0) + w^2Y(s) = s/(s^2 + 1). Right side is...

Homework Statement Solve the differential equation using laplace transforms. Assume zero intial conditions and that the forcing functions are zero prior to t=0 x''(t) + 6x'(t) +8x(t)=sin3t Homework Equations The Attempt at a Solution I took the laplace transform which I found to be after...

Hello, I'am looking for de correct transformation formule:\mathcal{L}[f(t).g'(t)] (and proof). I'am not looking for method to solve it by means of integrating g'(t), offcourse this a possible way. But assume that g(t) is much work to calculate. So is there a good one to one formule...

Homework Statement http://gyazo.com/22f5c655071e49adf3f4652e8042873b I derived the proof myself, but by arbitrary changing the t limit to infinity. I'm hoping that by understanding the diagram in the link above I will have a better idea of why I changed the limit. I currently look at it...

Say you find the laplace transform V(s) and want to switch it back to the time domain, once you've done this, how do you determine which parts of the total solution correspond to the complementary solution and particular solution respectively? Do you just find which parts approach zero as time...

Homework Statement Determine the capacitor voltage in the laplace domain. Homework Equations http://picturepush.com/public/8001507 http://picturepush.com/public/8001507 The Attempt at a Solution http://picturepush.com/public/8001546 http://picturepush.com/public/8001546 Using nodal...

[FONT=tahoma]A metallic spherical shell occupying the region given in terms of spherical polar coordinates \( (r, \theta, \phi)\) by \(r \le a \) has its surface \(r = a\) maintained at temperature [FONT=CMR12] [FONT=tahoma]\(u(a,\theta)=1 + \cos(\theta)+2 \cos^2(\theta) \) [FONT=tahoma]...

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...

(I hope I have posted this in the appropriate forum. I have consulted the posting guidelines and this seems to be OK. The subject of my post certainly isn’t homework or academic coursework, rather it is self-study for its own sake. If this is the wrong place – apologies, and maybe an admin could...

Hi, I am trying to derive one transfer function for a system, but got stuck at a point. I want the solution to the ratio V_o(s)/V_g(s), the transfer function. V_o(s) = [a*L{(V_g)^2} - b*L{V_o * (V_g)^2} - c*V_g(s) - d/s]*z(s) In the following equation, I have: s-> lapace transform...

Heat Equation (Non Homogeneous BCs) - Difficult Laplace Transform... help! ;) Hi I'm trying to model the temperature profile of an inertia friction welding during and after welding. I have the welding outputs and have come up with a net heat flow wrt time during the process. I now want to...

Homework Statement W(x,s)=(1/s)*(sinh(x*s^0.5))/(sinh(s^0.5)) Find the inverse laplace transform of W(x,s), i.e. find w(x,t). Answer: w(x,t)= x + Ʃ ((-1)^n)/n) * e^(-t*(n*pi)^2) * sin(n*pi*x) summing between from n=1 to ∞ Homework Equations An asymptotic series..?! The...

Homework Statement Determine the Laplace transform: g(t) = 2*e^{-4t}u(t-1) The Attempt at a Solution Essentially we're told for a time shift we multiply the Laplace transform pair of the function (without the delay) by e^{-as} So here a = 1 (for the delay) The Laplace transform for e^{-4t}...

I'm attempting to find the inverse laplace transform of \frac{25}{(1-s)^2*(4+s^2)} I get to this point but can't get the values of A B and C when equating coefficients. 25/(s-1)=A(4+s^2)+(Bs+C)(s-1) Also for a separate question: (s+1)/(5-4s+s^2) How do you find the inverse...

Homework Statement Here's the question: Use laplace transforms to find X(t), Y(t) and Z(t) given that: X'+Y'=Y+Z Y'+Z'=X+Z X'+Z'=X+Y subject to the boundary conditions X(0)=2, Y(0)=-3,Z(0)=1. Now I have learned the basics of laplace transforms, but have not seen a question in...

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 multiple choice question Homework Equations The Attempt at a Solution I inversed laplaced the problem and i get an answer of 3 H(t-3) sin(9(t-3)) which isn't any of the options so I chose F but that was wrong. So far I've confidentally...

Homework Statement question is attached Homework Equations L(1) = 1 /s L(t^n) = n!/s^(n+1) L{f '(t)} = s F(s) - f(0) L{f ''(t)} = s^2 F(s) - s f(0) - f '(0) The Attempt at a Solution okay so i laplace transformed both sides and i got: (s^2) Y(s) + 5s -5 -5s Y(s) -25 - 6Y(s) = -84exp(-5s) /...

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) =...

Use Laplace to solve x''+3x'+5x=sin(8t) Initial conditions x(0)= 2 and x'= -3 I have worked it down to (s2+3s+5)X(s)= 2s+3+ [8/(s2+64)] but stuck. Please help

Homework Statement Having found the laplace transform of a differential equation. I must now find X(t). All of my work is attached. The problem I am having is fitting my function of s to my table of transforms. I tried using partial fractions but it took me in a loop.The Attempt at a Solution...

Homework Statement Hey guys, I've attached the question that's troubling me. I've also attached the table and formulas of Laplace transform for you convenience. Homework Equations attached The Attempt at a Solution Right now, I am thinking the best way to do this problem is...

Hey guys, I have a butterworth high-pass filter, and I was asked to find it's temporal response equation to the u(t) function. That part was easy, using basic Laplace tables I was able to find the following equation: y(t)=√2 e^(-31100t) *cos⁡(31000t+π/4)u(t) However, I'm supposed to be able to...

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 We have been given a table of laplace transforms and have been asked to show them using the definition. ∫0∞e-stf(t)dt. But this one I have no clue where to begin ∫0tf(t)dt the laplace transform of this is F(s)/s. Can anyone tell me what to do with this one? Thank you...

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)...

Homework Statement Could someone please explain this to me? I have read several notes on it, but do not really follow the reasoning: The Attempt at a Solution When t = 0, -1/s*e^-st = -1/s because e^0 = 1. When t goes to infinity is the part I do not fully understand. Why...

Thought it's pretty related to this forum. I'm familiar with applications of both Laplace and Fourier in physics and differential equations. However I still struggling trying to figure out the intuitive interpretation of both transforms or at least a mathematical illustration that shows their...

Given $\begin{aligned} & {{u}_{t}}={{u}_{xx}},\text{ }x>0,\text{ }t>0 \\ & u(x,0)={{u}_{0}}, \\ & {{u}_{x}}(0,t)=u(0,t). \end{aligned} $ I need to apply the Laplace transform to solve it. I'll denote $u(x,s)=\mathcal L(u(x,\cdot))(s),$ so for the first line I have $s\cdot...

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 Homework Equations The Attempt at a Solution We went over the Laplace transformation today in my DE course. We only covered essentially, "how to do it", so: L(f(t)) = \int_{0}^{\infty}f(t)e^{-st}dt (also, how do you make the fancy f and curly brackets in Latex?)...

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...

Hi everyone, I have a problem with finding the transfer function of a linear system. It happens that in some terms the input and the output are multiplying and I have no idea how to do the Laplace transform of this. The system is a car and I am only studying its speed. The input is the...

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...

Homework Statement Find the inverse laplace transform of \frac{3s + 7}{s^{2} - 2s + 10}Homework Equations completing the square. e^{at}sin(bt) = \frac{b}{(s-a)^{2} + b^{2}} e^{at}cos(bt) = \frac{s-a}{(s-a)^{2} + b^{2}} The Attempt at a Solution F(s)= \frac{3s + 7}{s^{2} - 2s + 10} F(s) =...

Homework Statement I'm trying to find the Laplace transform of tJ''0(t), it's from bessels equation, but that doesn't matter too much at the moment, I just need to integrate (e^-st)*t*J''0(t) but am unsure how to go about this with the J''0(t) in there.

Sorry for thumb terminology, I just would like to grasp the main idea, as a physicist, without unnecessary complications, associated with system of axioms and definitions. Fourier transform can be seen as rotation of basis in space of all complex-valued functions from basis of delta-functions...

Using the laplace transform, find the solution to the differential equation: y'' + y' + y = 0 , y(0)=0, y'(0)=1 Using the laplace transform and its properties I end up with: f(s) = 1/(s2+s+1) How can I find the inverse of this/ does anyone know the inverse of it? Setting y=eax I got a...

How do I find the Laplace transform of 1 using MATLAB? >> laplace(1) gives the error ? Undefined function or method 'laplace' for input arguments of type 'double'.

Find the inverse Laplace transform of $\displaystyle \frac{2s+7-e^{-2s}}{(s+1)^2}$.

Find the Laplace transform of $\displaystyle f(t)=1$ if $\displaystyle 1\le t\le 4$; $\displaystyle f(t)=0$ if $\displaystyle t<1$ or if $\displaystyle t>4$.

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...

Homework Statement Solve the Laplace equation in one dimension (x, i.e. (∂^2h)/(∂x^2)= 0) Boundary conditions are as follows: h= 1m @ x=0m h= 13m @ x=10m For 0≤x≤5 K1= 6ms^-1 For 5≤x≤10 K2 = 3ms^-1 What is the head at x = 3, x = 5, and x = 8? What is the Darcy velocity...

Homework Statement I'd like to solve a DE using Laplace transform. \ddot y (t)+\omega ^2 y(t)=f(t) for all t>0. Initial conditions: y(0)=\dot y (0)=0. The dot denotes the derivative with respect to t. Homework Equations \mathbb{L}( \dot y )=s\mathbb{L}( y )-y(0). Convolution: if h=f*g...