Laplace transform Definition and 779 Threads

Hi all According to the textbook Signal and Systems by Oppenheim (2nd edition) pages 685 and 686, if the Laplace transform of x(t) is X(s) with ROC (region of convergence) R, then the Laplace transform of x(at) is (1/|a|)X(s/a) with ROC R/a. Consequently, for a>1, there is a compression...

Homework Statement L{2t u(t-1)} Homework Equations L{g(t) u(t-c)} = e^-cs L{g(t+c)} The Attempt at a Solution L{2t u(t-1)}=e^-s L{2(t+1)} L{2(t+1)}=2/s^2+2/s L{2t u(t-1)} = e^-s {2/s^2 + 2/s} i think the whole attempt is wrong , I'm getting confused in this type of...

Homework Statement just trying to get the below equation in terms of step functions, just not sure how to get the cos(t) with the same shifted variable f(t) = 0 for t<2 f(t)=cos(t) t>=2 The Attempt at a Solution this is what i got cos(t)u(t-2) just having troubles working out the...

[Solved] Laplace Transform Homework Statement \frac{d^{2}y}{dt^{2}}+4y=sin(t),\quad y(0)=0,\quad\frac{dy}{dt}(0)=0 Homework Equations Laplace transform is defined as: \mathcal{L}\{f(t)\} = \int_{-\infty}^{\infty}f(t)e^{st}dt The Attempt at a Solution...

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Homework Statement F(s) = (s + 1)/(s2 + 1)2 Homework Equations The Attempt at a Solution I used partial fractions but I still end up with a term that includes a (s^2 + 1)^2 in the denominator. I'm pretty much lost at this point.

Homework Statement Solve the differential equation: y'' + 4y' + 4y = delta_3 (t) y(0) = 0 and y'(0) = 1Homework Equations 1) lapace [delta_a] = e^-as 2) laplace inverse [ 1 / (s+a)^n] = [(t^n-1) / (n-1)! ] *e^-atThe Attempt at a Solution so I began by taking the laplace transform of both...

Homework Statement Find the inverse laplace transform of: 1/(s-2)3 + 25/(s+1)(s-2)2 + s/(s-2)2 The attempt at a solution I get (1/2)e2tt2 + (25/7)e-t-(25/7)e2t+(75/7)te2t for the first two, but I'm not even sure where to start for s/(s-2)2. I was thinking it might use...

http://img215.imageshack.us/i/unledc.jpg/ Using the residue method, I found K1 and K2 to be -2 and 4 respectively. However, where do I go from there?

Homework Statement I need to know what the laplace transform is for f(t) * u(t) More specifically, h(t) = cos(3t)*u(t) Homework Equations I know that f(t-to) * u(t-to) = e-tos * F(s)The Attempt at a Solution So, f(t) = cos(3t) F(s) = s/(s2 + 9) In the formula I gave in (2), I would...

Can some one help me to understand this: I need to use the second shifting theorem to get the Laplace transform, given: f(t) = { 4 - t2 , t < 2 ...... 1 { 0 , t >= 2 They got this: f(t) = (4 - t2)(1 - u(t - 2)) .... 2 I know that the...

Homework Statement Use the First Shifting Theorem (translation on the s axis) to find f(t). L-1[(2s-1)/(s2(s+1)3] Homework Equations The Attempt at a Solution This is going to take forever.. Can we assume that I am putting the L^-1 all over the place? [(2s-1)/(s^2(s+1)^3)] =...

Homework Statement The signal x(t) = u(t-1) - u(t-3) is the input to an LTI system with the impulse response h(t) = u(t-5) - u(t-8). the system is initially at rest. a) Compute the output y(t) of this system using convolution. b) Compute the output y(t) of this system using the Laplace...

Homework Statement [PLAIN]http://img340.imageshack.us/img340/8508/circuit.png Find V2(s)/V1(s) (Laplace transform domain) Homework Equations KCL, capacitor equation. The Attempt at a Solution \frac {-V_2}{R} + \frac {V_1-V_2}{R} + C \frac {d(V_1-V_2)}{dt}=0 But in Laplace domain it follows...

Homework Statement F(s) = (2s2 + 20s + 36) / (s3 + 6s2 + 9s) Homework Equations L[e-at] = 1 / (s + a) L-1[(s+a) / ((s+a)2 + w2)] = e-atcos(wt) L-1[w / ((s+a)2 + w2)] = e-atsin(wt) The Attempt at a Solution Factored the top by 2 and the bottom by s, but the rest of the top seems...

Homework Statement Well i did all my work but the forum logged me out and when i submitted it I lost it all because it wanted me to login again >_< anyways i need to find the inverse laplace transform of F(s)=[12*s^2 - (28+2*sqrt(3))*s + 26 + 6*sqrt(3)]/[(s-3)(s^2-2s+2)] Homework...

This is my first time posting on these boards, so forgive me if I am posting incorrectly or in the wrong forum. I have been able to successfully work through problems with forcing functions of constant value "steps", but am having trouble working with those with linear portions of the...

I do not have trouble doing these types of problems if the domains are not equalities. However for this type of problem.. f(t)= 0 , t=2 t , t\neq 2 (I do not know how to do piecewise function in latex) I figured this is on the right track... t-tu_{2}(t)+2tu_{3} I have a problem...

Homework Statement ((d^2)x)/(d(t^2)) + 5(dx/dt) + 6x = f(t) f(t)=3 for (0<=t<6) f(t)=0 for t>=6 Homework Equations This I am not sure of, this is my question. Would I use the Second Order Differential equation to do this problem: L{((d^2)f)/(d(t^2))} = (s^2)F(s) - sf(0") -...

Homework Statement I'm working on some Differential Equations homework and I'm stuck. The question is apply the translation theorem to find the Laplace transform. f(t) = e^(-t/2)cos2(t-1/8π) I know how to apply the method, I just need to figure out how to transform the cosine...

can someone please help me find the inverse laplace transform of the following: http://www.webpagescreenshot.info/img/694286-34201141544am.png i do not know how to solve for this due to the e^-20s shift in the denominator... is there a way to change this function to make it easier to solve?

What is the laplace transform of a function that is 1 from 0 to 10 and 0 elsewhere? I know that this can be represented by the step function U(10-t)U(t)...but how do i find the laplace transform of this?

So, the definition of Laplace transform is: \int_{0}^{\infty} e^{-st} f(t) dt what if: f(t) = g(t)exp\Big[-\int_{0}^{t}g(t')dt'}\Big] Or, in words: if the function being transformed is itself a function of an integral. This seems somewhat tough, but maybe I just...

Hi, all. I am doing an inverse Laplace transform and meeting some difficulty. InverseLaplaceTransform[1/(Sqrt[s]+a)]. Using Mathematica I found the result, however, I failed to prove it. I know it should be like \frac{1}{2\pi i}\int_{\gamma-i\infty}^{\gamma+i\infty} \frac{1}{\sqrt{s}+a}ds...

I have two subsystems that I'm trying to transform into the frequency domain, and trying to obtain the transfer function for each. I have an equation (for system 1) m\ddot{x} -k(x2-x1) - b*\dot{x}1 = f Since this is for system 1, when I take the laplace transform of it, do i have x2 as...

i need help trying to find the laplace transform of te-t\delta(t) i know the laplace transform of te-t is 1/(s+1)2 but i don't know how to find the laplace transform of a product with the Dirac delta

what is the Laplace transform of sin2(t-1)U(t-1) (U is the unit step function) i got 2e-s/s2 + 4 is this correct? i'm unsure about the exponential part

Homework Statement I already got Q(s)=150/(s(s^2+20s+200)), then i complete the square on the quadratic. I got Q(s)=150/(s((s+10)^2+10^2))). But then i can't find the Q(t) because the equation (s+10)^2+10^2=0 dosent have roots. Or i have to use complex numbers ? So I am confused...

Homework Statement The question is solve using laplace transforms: y" - 4y = 1-2t where y(0) =0 and y'(0) = 0 Ans is: y = t/2 - 1/4 + 1/4*e^(-2t) Homework Equations http://www.stanford.edu/~boyd/ee102/laplace-table.pdf" partial fractionsThe Attempt at a Solution (s^2)Y - sy(0) - y'(0) - 4Y =...

So my professor is really bad and I've had to try to learn to learn this stuff myself. But I have no idea where to start and where to go. Problem: X(s) = \frac{3(3s+2)}{9s^{2}+12s+4}Attempt All I've been able to figure out so far is: -> X(s) = \frac{3}{(3s+2)^{2}} * \frac{1}{(3s+2)}} But...

show that L{f(t/b)} = bF(bs), b is not equal to 0 i know that L{f(t)} = \inte-stf(t) dt = F(s) so L{f(t/b)} = \inte-stf(t/b) dt any tips on how to start? thx

Homework Statement Find the Laplace transform of f(t) x cos(t) (multiplication) if the Laplace transform of f(t) is F(s). Homework Equations The Attempt at a Solution I'm pretty sure I am supposed to use the second equation, however I do not understand how to use it. If you...

I wonder does anyone have a source for the derivation of the Laplace transform in print that is analogous to the derivation given in this video: https://www.youtube.com/watch?v=zvbdoSeGAgI https://www.youtube.com/watch?v=hqOboV2jgVo I've browsed booksgoogle but have really been unable to...

Homework Statement Compute Y(t). Homework Equations Y(s)= (s(2s+11)+ω(8s+4ω^2))/((s^2+ω^2)(s+9)(s+2)) The Attempt at a Solution (s(2s+11)+ω(8s+4ω^2 ))/((s^2+ω^2)(s+9)(s+2))= A/(s^2+ω^2 )+B/(s+9)+C/(s+2) Every example I have looked at does not have the ω variable, but I...

Does anyone recognize this expression for the pressure: p(T,\mu) = T s^*(T,\mu) where s^* is the extreme right singularity in the Laplace transform of the grand canonical partion function. If someone knows this, I am curious in the derivation, and in what cases it is applicable. (In the...

Ok...so this isn't homework (well past that at 39!) but I'm trying to brush off the old cobwebs and solve a vehicle motion problem. Specically, I'm trying to find the Homework Statement Ok...so this isn't homework (well past that at 39!) but I'm trying to brush off the old cobwebs and...

Homework Statement Find the inverse Laplace Transform for the function, F(s) = \frac{(3s^{2}+9s+14)e^{-5s}}{s^3 + 4s^2 +7s} Homework Equations The Attempt at a Solution We are given a table of common laplace transforms that we are allowed use to without proof. First I'll...

I'm trying to prepare for an exam and we were warned that the Laplace transforms given to us may have Complex roots, double roots, or double complex roots. I'm comfortable with complex roots, but I can't find a problem in the textbook that deals with double roots, and I haven't used them since...

Hey Guys. Im trying to find an inverse laplace transform for fraction in the laplace domain but can't find it in any of my laplace pair tables. The fraction is: 1/(s + 4)(s + 4)(s + 8) Does anybody have any suggestions?

Please help me explain how to solve this to find the unilateral laplace transform x(t)=tu(t) - (t-1)u(t-1) - (t-2)u(t-2) + (t-3)u(t-3) I know the part tu(t) as a(t) = u(t) --> 1/s then b(t) = tu(t) ---> - d/dx a(t) = 1/s^2 But for those (t-1), (t-2) in front u(t), how to solve...

Homework Statement Find the inverse Laplace Trasnform of, F(s) = \frac{s^{2}}{(s^{2} + 9)^{2}} Homework Equations The Attempt at a Solution We are given a table with a bunch of common Laplace transforms and their inverses but I can't seem to get this one. Can anyone nudge...

Homework Statement Find the Laplace Transform from the definition of f(t) = tcos(2t) Homework Equations \int e^-^s^ttcos(2t)dt The Attempt at a Solution I started by doing parts u = t du = dt dv = cos(2t)e^-^s^t dt but I get stuck on v and as far as I can tell doing parts...

Homework Statement I'm trying to take the laplace transfrom of t H(t) where H(t) is the unit step function. Also, in a separate problem I get e^{-t} H(t) - e^{-t}H(t-1) and I am wondering how to manipulate it properly Homework Equations L \{ f(t-a) H(t-a) \} = e^{as}F(s) The...

1. find the Laplace transform of \sqrt{t/pi}cos(8t). 2. Tried to look at the tables and combine things but I'm not very sure where to start.

Homework Statement Find the Laplace transform of the time function using the integral definition: g(t) = e-a(t+T)*u(t+T) Homework Equations Laplace transform definition The Attempt at a Solution After working through it, I was curious to see if the answer I received is, in...

dx/dt= -x+y dy/dt= 2x x(0)=0 y(0)=1 I'm not familiar how to solve a system like this. Somebody please help? Thanks

Homework Statement y'+2y=f(t), y(0)=0, where f(t)=\left\{t, 0\leq t<0 \;and \; 0, t \geq 0 (I don't know how to do piecewise)Homework Equations Equation for initial conditions; step function: u(t-a) The Attempt at a Solution I know how to solve a differential equation with initial...

Can anybody show me how to prove this Laplace transform which leads to a complimentary error function? Thanks!\int^\infty_0 \frac{\sqrt{a}}{\pi \sqrt{x} (x+a)} e^{-x} dx = e^a erfc(\sqrt{a})I don't know how to separate a factor of \sqrt{\pi} from the laplace transform.

Homework Statement Y' + 8y = e^-2t*sint, with initial condition y(0) = 0 Homework Equations L{e^(-2t)sin(t)} = 1/((s+2)²+1) The Attempt at a Solution Alright so I've been working on this one for about an hour, I really don't know why but I'm having major problems with these types...

Homework Statement solve the following differential equation using laplace transform: dy/dt+yx=0 y=20 when x=0 Homework Equations The Attempt at a Solution I took the laplace for each term L(dy/dx)= s*Y(s)-y(0) L(xy)=X(s)Y(s) subtitute back to the equation...