Laplace transform Definition and 752 Threads

I am engineering student and studying signal processing. The term Fourier transform comes in the discussion several times. There are many transforms like Laplace transform,Z transform,Wavelet transform.But as per my view ,Fourier transform is mostly used compared to others in general. My...

23.) y'' + 2y' + y = 4e-t; y(0) = 2, y'(0) = -1 Y(s) = [(as + b) y(0) + a y'(0) + F(s)]/(as2 + bs + c) My attempt: a = 1, b = 2, c = 1 F(s) = 4 L{ e-t } = 4/(s+1) (From Laplace Transform Table) Plugging and simplifying: Y(s) = (2s2 + 5s + 7)/[(s + 1)(s2 + 2s + 1) Here is where I get...

Homework Statement f(t) = e^t when 0≤t<1 and 0 when t≥1 Homework Equations Laplace transformations The Attempt at a Solution so the Laplace integral becomesfrom 0 to 1 ∫e^(st^2)dt + 0 how do I integrate this?

Homework Statement How can I take the Inverse Laplace Transform of $F(s) = \frac{d}{ds}\left(\frac{1-e^{5s}}{s}\right)$? I have tried going with inverse of the derivative and convolution (even tried evaluating the derivative and go from there) but although I can get to some results none of them...

Solve by Laplace Transforms. So I'm stuck on how to find this $$\mathcal{L}^{-1}$$ $( \frac{\frac{5s}{4} + \frac{13}{4}}{s^2+5s+8} ) $ I'm not sure what t odo. I was thinking I need to use the $\cos(at)$ and $\sin(at)$ formulas but I'm not sure... Any help would be great

Solve by Laplace Transforms. $y'' + 4y' + 4y = e^t$ $y(0) = 1$, $y'(0) = 0$So I've got $s^2Y - s + 4sY - 1 + 4Y = \frac{1}{s+1}$ then I got: $ Y = \frac{s^2+2s+2}{(s+2)(s+2)}$ Now here is where I am getting lost on the partial fraction decomposition.. I've got $s^2+2s+2 = A(s+2) + B$ I...

I was wondering whether this can be done: Let's say you have transfer function that goes like this: \frac{Y(s)}{U(s)}= \frac{N(s)}{D(s)} Now let's say I divide my transfer into two: \frac{Y(s)}{Z(s)}= N(s) \frac{Z(s)}{U(s)}= \frac{1}{D(s)} Can I apply the Laplace Inverse to these two...

in an example in my text i don't see how they got the "sU" for the transform. actually, i don't even see it in my table of transforms.

Hello PF! We were doing mass balances on mixing tanks in one of my ChemE courses, and in one of the problems we arrived at the following DE: \frac{dC_B}{d \theta} + 0.025C_B=0.0125 e^{-0.025 \theta} Where CB is the concetration of salt in the tank and θ is time. The professor made us solve the...

And also: y`+2y=2(1-e^-2t) Y(0)=0 y¨-2y`+y = t+e^t y(0)=1 and y`(0)=0 Please help me out here folks ;)

Hi. I`m new here and I need some help with Inverse Laplace Transform: f(t)=5+3t+e^3t g(t)=(t+1)u(t-2) g(t)=(t^2-9t+20)u(t-5) and Laplace Transform: F(s)=1/(s+2)^5 F(s)= 2s^2+10/s(s^2+2s+10) G(S)=2s/s^2+4e^-sso if anywone can please help me:)

Hi, Please I need some help, how can I get the Laplace transform of the integration of a difference equation?? $\int _{ 0 }^{ \infty }{ { e }^{ -st } } \int _{ -\tau }^{ 0 }{ G(\theta )x(t+\theta )d\theta } dt$ Many thanks in advanced.

I need to know what's the Residue Theorem for a Laplace Transform. Does anyone know the name or something, so I can search it? I couldn't find anything. For example, if I have this two equations: X(s).(s-1) = -Y(s)+5 Y(s).(s-4) = 2.X(s)+7 I know how to solve them using Simple Fractions, but...

Hi everyone! :) Have a problem here I can't solve atm. Solve the Laplace transform, when: My try: Would really appreciate some help!

Hello everyone, I have a question about integrating in Laplace Transform. For example, if I have: f(t)=e^{i.t} I have to solve this equation: \int_{0}^{\infty}e^{i.t}.e^{-s.t}dt If I do like this, it's very simple...

Homework Statement use laplace transforms to solve the differential equation y"+2y'+17y = 1 Homework Equations Initial conditions are y(0) = 0 y'(0) = 0 The Attempt at a Solution so it converts to Y(s) (s^2+2s+17) = 1/s which then ends up as; Y(s) = 1/s*1/(s^2+2s+17) i know i need to invert...

Homework Statement solve the following differential equation using Laplace transforms: y'' + 4y' + 4y = t^2 e^{-2t}, y_0 = 0, y'_0 = 0 y_0 and y'_0 are initial conditions. Homework Equations Using L to represent the Laplace transform, we have that L(y) = Y L(y') = pY - y_0 L(y'') =...

Homework Statement take inverse laplace of: 6/[s^4(s-2)^2] Homework Equations 6/[s^4(s-2)^2] The Attempt at a Solution I used partial fractions. I was wondering if It could be manipulated to where I could use the laplace table?

Homework Statement Find H(s) = \frac{Y(s)}{X(s)} \frac {d^2y(t)}{dt^2} + a\frac {dy(t)}{dt} = x(t) + by(t) Homework EquationsThe Attempt at a Solution [s^2 + as - b] Y(s) = X(s) H(s) = \frac{1}{s^2+as-b} I assume the inverse is a sign or a cosine but unsure which one.

Homework Statement I do not know how to find f(t) with the given Ampliture 40 and a=pi Homework EquationsThe Attempt at a Solution I have the solution above. my set up was 1/2y''+y'+5=f(t) 1/2S^2* Y(s) + Y(s)+5=f(t)

Homework Statement I'm given a transfer function C(s)=10R(s)/(s+4) And I have to find c(t) for r(t)=6u(t) The Attempt at a Solution First I did this problem by taking inverse laplace of the transfer function, and inserting the value of r(t) in it. Next I did the same problem by first...

Homework Statement Solve the integral y(t) + \int_0^t (t-u)y(u) \, du = 3sin(2t) Homework EquationsThe Attempt at a Solution Rewrite the equation: y(t) = 3sin(2t) - \int_0^t (t-u)y(u) \, du I assume the integral to be the convolution: f(t) * y(t) = t * y(t) as f(t-u) = f(t) = t...

Homework Statement Solve the IVP : dy/dt + y = f(t) y(0) = -5 where f(t) = -1, 0 <= t < 7 -5, t >= 7 y(t) for 0 <= t < 7 = ? y(t) for t >= 7 = ? Homework EquationsThe Attempt at a Solution So I have never seen a problem of this type, excuse my silly mistakes if I'm interpreting this question...

Homework Statement Determine the Laplace transform of the given function: f(t) = sin(t) for 0 <= t < \pi and f(t) = 0 for \pi <= t Homework EquationsThe Attempt at a Solution Ok, I've been having some trouble figuring out how I should write the above branched function (sorry for the...

Inverse Laplace transform \mathcal{L}^{-1}[F(p)]=\frac{1}{2\pi i}\int^{c+i\infty}_{c-i\infty}F(s)e^{st}dp=f(t) Question if we integrate along a straight line in complex plane where axis are Re(p), Im(p), why we integrate from c-i \ínfty to c+\infty? So my question is, because Im(p) are also...

Homework Statement Find L[x(t)], where $$ x(t) = tu(t) + 3e^{-1}u(-t) $$ Also determine the region of convergenceHomework EquationsLaplace properties, Laplace table: L[te-at = 1/(s+a)2 L[u(t)] = 1/s L[t] = 1/s2 The Attempt at a Solution I don't really know what to do with this as my table...

Homework Statement Division by s Equals integration by t: For this problem use the following property (see relevant equations) to find the inverse transform of the given function: F(s) = \frac{1}{s(s-1)} Homework Equations L^{-1}(\frac{F(s)}{s}) = \int_{0}^{t} f(\tau)\,d \tau The Attempt...

Homework Statement If L[x(t)] = (s + 4)/(s2 + 1), find L[tx(t)] Homework Equations Laplace transform: F(s) = 0∫ f(t)e-stdtLaplace table The Attempt at a Solution Clearly it's not just asking for a Laplace transform. Not sure what it's specifically asking to be honest. t multiplied by...

Homework Statement x(t) = cos(3πt) h(t) = e-2tu(t) Find y(t) = x(t) * h(t) (ie convolution) Homework Equations Y(s) = X(s)H(s) and then take inverse laplace tranform of Y(s) The Attempt at a Solution L(x(t)) = \frac{s}{s^2+9π^2} L(h(t)) = \frac{1}{s+2} I then try to find the partial...

Homework Statement A 4-pound weight stretches a spring 2 feet. The weight is released from rest 15 inches above the equilibrium position, and the resulting motion takes place in a medium offering a damping force numerically equal to 7/8 times the instantaneous velocity. Use the Laplace...

Homework Statement x(t) = cos(3πt) h(t) = e-2tu(t) Find y(t) = x(t) * h(t) (ie convolution) Homework Equations Y(s) = X(s)H(s) and then take inverse laplace tranform of Y(s) The Attempt at a Solution L(x(t)) = [πδ(ω - 3π) + πδ(ω + 3π)] L(h(t)) = \frac{1}{s+2} Laplace Transform inverse ...

Homework Statement I keep getting the wrong answer, and wolphram seems to back me up. Here's the system of equations ##(-10+s)X(s)-7Y(s)=\frac{10}{s}## ##X(s)+(-2+s)Y(s)=0## Homework EquationsThe Attempt at a Solution Using Cramer's rule I've got...

Find the LT and specify ROC of: x(t) = e-at, 0 ≤ t ≤ T = 0, elsewhere where a > 0 Attempt: X(s) = - 1/(s+a)*e-(s+a) integrated from 0 to T => -1/(s+a)[e-(s+a) + 1] Converges to X(s) = 1/(s+a) , a ⊂ R, if Re{s} > -a for 0≤t≤T Elsewhere ROC is empty (LT doesn't exist). Is this...

Mod note: Please don't tinker with SIZE tags. Things are perfectly readable without them. Homework Statement Find x(t) = L-1[(4e-4s - 3)/(s2 + 6s + 25)]. Homework Equations L(x(t)) = ∞∫∞x(t)e-stdt L-1(x(s)) = (1/2π)(σ - ∞j)∫(σ + ∞j)[x(s)est]ds, "But you want to avoid this integral." Laplace...

<< Moderator Note -- thread moved to the Homework Help forums >>[/color] I'm stuck on a problem, and I'm in serious need of help. I) Problem: Find the solution to f (t) = 2 \int^t_0 f'(u) sin 3 (t-u) \ du + 2 cos (3t) . Also find f (0) .II) Solution, so far: F(s) = 2 (s F(s) - f(0)) *...

Hello everyone, I have spend whole day but still not figure out an inverse Laplace transform. Hope someone can help me. The question is in the attachment. I'm trying to extract u^2/4D^2 out the bracket to match the standard inverse table, but it seems difficult to deal with the square root...

Homework Statement we have to solve the given circuit using laplace transform for i(t) for t>0 when switch k opened at t=0.. now all I wnated to make clear is the final circuit diagram of this in s-domain..[/B]Homework EquationsThe Attempt at a Solution as I solved I considered the circuit to...

Homework Statement Wondering if I did this correctly.. Find the laplace transform: $$z(t)=e^{-6t}sin(\omega_{1}t)+e^{4t}cos(\omega_{2}t)$$ for ##t\geq 0## Homework Equations The Attempt at a Solution For the first part, I assume I can do this, but I'm not too sure. This is my main question...

please check my work here $\mathscr{L}[2\sin(bt)\sinh(bt)]$ I know that $\sinh(bt) = \frac{e^{bt}-e^{-bt}}{2}$$\mathscr{L}[2\sin(bt)\left(\frac{e^{bt}-e^{-bt}}{2}\right)]$...

Homework Statement Decide the inverse laplace transform of the problem below: F(s)= \frac{4s-5}{s^2-4s+8} You're allowed to use s shifting. Homework Equations The Attempt at a Solution By looking at the denominator, I see that it might be factorized easily, so I try that...

Homework Statement Find the inverse Laplace transform of the expression: F(S) = \frac{3s+5}{s^2 +9} Homework Equations The Attempt at a Solution From general Laplace transforms, I see a pattern with laplace transforming sin(t) and cos(t) because: L{sin(t)+cos(t)} =...

I took an introduction to ODEs course this past spring semester. It always bothered me where this thing came from. I did a little bit of research and found a video of a professor explaining how it is the continuous analog of an infinite sum. He did a little bit of a derivation using that...

1. why do we need to use shifted unit step function in defining second shifting theorem? 2. why don't we instead calculate laplace transform of a time shifted function just by replacing t by t-a? 3. everywhere in the books as well as internet i see second shifting theorem defined for...

Firstly, if this is an inappropriate forum for this thread, feel free to move it. This is a calculus-y equation related to differential equations, but I don't believe it's strictly a differential equation. The question I'm asking is which functions...

Homework Statement Hi. I need help to resolve the inverse laplace transform of {1/((x^2)+1)^2}2. The attempt at a solution I have tried to do: {(1/((x^2)+1) * (1/((x^2)+1)} then, convolution, sen x But, isn't working Thanks for your help :)

Hi All, I'm playing around with an arduino, and have build a PID controller that controls the temperature of a light bulb, measured with an NTC. All is working fine I'm looking to get a bit more theoretical on the subject and have modeled the system in a simulink like environment. I want...

Homework Statement Ds + E / (s^2 +1)^2 Homework Equations The Attempt at a Solution Ds / (s^2 +1) + E / (s^2 +1) D[s/(s^2 + 1)^2] + E [1 / (s^2 + 1)^2]

before I go to bed(it's 11:30pm in my place), here is the last problem that I need help with find the inverse Laplace Transform $\frac{4s-2}{s^2-6s+18}$ the denominator is a non-factorable quadratic. I don't know what to do. thanks!

find the inverse Laplace of the ff: 1. $\frac{n\pi L}{L^2s^2+n^2 \pi^{2}}$ 2. $\frac{18s-12}{9s^2-1}$ for the 2nd prob I did partial fractions $\frac{18s-12}{9s^2-1}=\frac{9}{3s+1}-\frac{3}{3s-1}$ $\mathscr{L}^{-1}\{\frac{18s-12}{9s^2-1}\} =...

$\mathscr{L}\{\sin^{2}4t\}$ $\mathscr{L}\{\sin(3t-\frac{1}{2}\}$for the 2nd prob here's what I have tried $\mathscr{L}\{\sin(3t)\cos(0.5)-\cos(3t)\sin(0.5)}$ $\cos(0.5)\mathscr{L}\{\sin(3t)\}-\sin(0.5) \mathscr{L}\{\cos(3t)\}$ $\frac{3\cos(0.5)-s\sin(0.5)}{s^2+9}$ ---> is this correct? for...