Laplace Definition and 1000 Threads

Homework Statement Obtain the solution of the differential equation x'' + w2nx = t My use of L refers to the Laplace Homework Equations The Attempt at a Solution L{x'' + w2nx = t} I decided to do the Laplace of each part individually starting with x'' L{x''} =...

Homework Statement Derive he Laplace Transform of the third derivative of f(t). Homework Equations The Attempt at a Solution So, I'm not at all sure how to do this. I think I can start with: L{f'''(t)} = But I'm honestly not sure how this works. Any guidance would be...

Homework Statement Obtain the Laplace transformation of the function defined by f(t) = 0 t<0 = t2e-at t>=0Homework Equations The Attempt at a Solution I'm a little unsure of what I'm doing here, so bear with me. L {t2e-at} = ∫inf0 t2e-at dt = ∫0inf t2e-(a+s)tdt How do I integrate...

Homework Statement Find the Laplace transformation of the following function by using iterations of integration by parts: f(t) = tsin(t) Homework Equations The Attempt at a Solution I know how to do integration by parts (as learned in calculus) but have never seen a funtion...

I am reviewing some material on Laplace Transforms, specifically in the context of solving PDEs, and have a question. Suppose I have an Inverse Laplace Transform of the form u(s,t)=e^((as^2+bs)t) where a,b<0. How can I invert this with respect to s, giving a function u(x,t)? Would the inverse...

I read from the PDE book about Laplace equation in static condition ie ##\frac {\partial U}{\partial t}=0##. But is it true that even if U is time varying ie ##U=U(x,y,z,t)##, you can still have Laplace and Poisson's equation at t=k where k is some fixed value. ie...

Homework Statement The Attempt at a Solution I know that u(t) is a unit step function and holds a value of either 0 or 1. In laplace transform, when we integrate f(t) from 0 to infinity, we take u(t) to be 1. In this case, since u(t) is u(-t), does this mean it holds a value of 0? Does not...

Homework Statement Find the inverse Laplace transform of e^(-3pi*s)/(s^2+2s+3). Homework Equations I know that you're supposed to factor out the e^(-3pi*s) and the other part becomes 1/(s+1)^2+2 but how do you get the answer? I'm confused. The Attempt at a Solution The answer is...

Homework Statement Find the Inverse Laplace Transform of \frac{1}{(s^{2} + 1)^{2}} Homework Equations The Attempt at a Solution I tried using partial fractions but it didn't work. It looks like a cosine transform, but I don't know what else to do. Help please :(

Hi All, in a previous post on the physical meaning of Laplace's Transform I found the following statement " The fundamental Laplace transform pair is H(t), the Heaviside step function, and 1/s, its spectrum of damped sinusoids. Note that the spectrum is weighted towards low frequencies...

This is more of a pre calc question but it dose however come from diff eqs, just in case I have made fundamental mistakes, i have posted it here. I have been studying this topic for few days by myself, never had any problems with algebra until here. really appreciate all of your help...

Homework Statement ##\int_0^\infty \frac{a}{a^2+x^2} dx## Homework Equations All the basic integration techniques. The Attempt at a Solution So, I saw this problem and wanted to try it using a different method then substitution, which can obviously solve it pretty easy. Since it is a very...

Homework Statement Find the inverse Laplace transform of F(s)=(8s^2-4s+12)/(s(s^2+4)). Homework Equations A/s+(Bs+C)/(s^2+4) 8s^2-4s+12=A(s^2+4)+(Bs+C)(s)=As^2+4A+Bs^2+Cs=s^2(A+B)+Cs+4A 8=A+B C=-4 A=3 B=5 L^-1 (3/s)+L^-1 ((5s-4)/(s^2+4)) =3+ (Now I'm stucked.) The Attempt...

Homework Statement Find the inverse Laplace transform of F(s)=(2s-3)/(s^2-4). Homework Equations I don't want to find the answer by looking at the Table. F(s)=2s/(s^2-4)-3/(s^2-4) The Attempt at a Solution The answer is f(t)=2 cosh 2t - (3/2) sinh 2t.

Hi, Basically I have circuit with an input Vi (s) across a capacitor C which is in parallel with a resistor R1. And these 2 components are in series with another resistor R2 (please see attached drawing). The question states: Show that the transfer function of the circuit is: Vo/Vi...

greetings, Can anyone tell me when we should use Laplace transform and Fourier transform? It seems both of them are equal except σ . thanks in advanced.

Homework Statement Solve the DE for y(t) with the IC's y(0)=20.8m/s and y'(0)=0 if the input is a step function scaled by the desired velocity Vo. vd(t)=Vou(t). Assume the desired velocity Vo=27.8m/s Homework Equations y''(t) + (D/M)y'(t) + (K/M)y(t) = (K/M)vd(t) M = 1,000kg D = 100kg/s K...

I attached the problem as a word document. I'm stuck trying to determine the laplace transform for t-tU(t-1). I know I'm supposed to work with 1/s^2(s+2) and solve for A, B,C. I got B=1/2, A=-1/4, and C=1/4 when 1=(As+B)(s+2)+Cs^2. The answer to the problem is y= 1/4 + 1/2t +1/4 e^-2t -[1/4...

Hey everyone, I've been reading up a bit on control systems theory, and needed to brush up a bit on my Laplace transforms. I know how to transform and invert the transform for pretty much every reasonable function, I don't have any technical issue with that. My only problem is that some...

Having difficulty with L-1 {1/(s^2+s-20)}: Should I make it L-1 {1/(s+5)(s-4)}? I'm stuck.

what is the inverse laplace transform of (2s)(1/(s-2))? could i use the identity ∫f(T)g(t-T)dT=F(s)G(s)? i was hesitant so i figured i'd just ask before i continue..

Here is the question. Here is a link to the question: Can you show the steps of this differential equations problem? - Yahoo! Answers I have posted a link there to this topic so the OP can find my response.

I found the following integral $$\int_{0}^{\infty} \, e^{-at} \sin(bt) \frac{\ln t}{t}\, dt $$ This thread will be dedicated to solve the integral , any ideas will always be welcomed (Cool). Serious steps will be made in the next threads . It seems to involve Laplace identities the value...

Homework Statement Homework Equations V(L)=L*di/dt laplace(u(t))=1/s The Attempt at a Solution was just wondering if i did this right. converted to the s domain, then wrote voltage equation around loop, in terms of current I(s): V(s)=R*I(s)+L(\frac{dI(s)}{dt}-iL(0-))...

In the attachment that I added I highlighted the portion I am questioning. I will define L[f(t)](s) to be the laplace transform of the function f(t). f(t) = e^t L[f(t)](s) = 1/(s-1). The laplace transform is defined for all values s≠1. L[f(t)](2) = 1. Question: "What do they mean by...

Homework Statement Laplace transform: te^t*H(t-1) Homework Equations L{te^t} = 1/(s-1)^2 L{H(t-1)} = e-s/s The Attempt at a Solution Using e^(at)f(t) -> F(s-a) with..e^(1t)H(t-1) We can get, e^(-1s-1)/(s-1) = e^(-s-1)/(s-1) [I think?] Thus applying tf(t) -> -dF/ds Derive[e^(-s-1)/(s-1)]...

Homework Statement y(t) solves the following IVP y''(t) + 2y'(t) + 10y(t) = r(t) y(0) = 2 y'(0) = 3 r(t) = 0 if t < 0 t if 0 ≤ t ≤ 1 0 if t > 1 Demonstrate that the laplace transform of y(t) is Y(s) = \frac{2s+7}{s^{2}+2s+7} + \frac{e^{-s}}{s(s^{2}+2s+7)} +...

Hi, Laplace transforms are a fundamental tool in electrical engineering and control systems engineering. Unfortunately my University is having us read books that use Laplace Transforms, but I've never learned the theory rigorously! For example the book I'm currently reading state briefly that...

I have two questions: I had to find the Laplace transform of: t \cdot sin(t) Not by definition, using a table of transforms and the properties. I did: sin(t) = i \cdot sinh(it) = i \cdot \frac{e^{t}}{2}-i \cdot \frac{e^{-t}}{2} Then t \cdot sin(t) = it \cdot \frac{e^{t}}{2}-it \cdot...

Hi there, I have my final in my circuit analysis class tomorrow morning(at a community college, it feels like two semesters worth of content was covered in 18 weeks). Last week, the teacher went over LaPlace Transform analysis rather quickly, and then onto basic digital logic. I do not...

Homework Statement Transform the given DE to find a nontrivial solution such that x(0)=0. tx''+(t-2)x'+x=0Homework Equations The Attempt at a Solution Using L{f(t)}=-\frac{1}{t}F'(s), I got 4sX(s)+s(s+1)X'(s)=0. I see that it is separable, but I do not know how to go about separating it...

Homework Statement Find the solution of the givien initial value problem and draw its graph y''+2y'+2y = δ(t-π) y(0) = 1, y'(0) = 0 Homework Equations A Laplace transform chart would be very useful The Attempt at a Solution I chose to solve the equation with Laplace...

Homework Statement (6-t)heaviside(t-2) This is just one term of the real problem I'm working, but it will serve to help me figure this out. Homework Equations The Attempt at a Solution http://www.wolframalpha.com/input/?i=laplace+transform+%7B%286-t%29heaviside%28t-2%29%7D...

Homework Statement The circuit below uses ideal components and disguises itself as a second order system when in fact it is really two first order systems. Prior to t=0 switch S is open. Then suddenly at t=0 switch S is closed. Find the peak output voltage V_{0max}, and the time taken for...

Recently in my DiffEq class, we learned how to use, and come up with, Laplace transforms. After doing my homework, I realized that Laplace Transforms are my new favorite concept in math(just beating out double/triple integrals and their applications)! The transforms just look so elegant on a...

Homework Statement \dfrac{\partial^2 \varphi }{ \partial x^2} - \dfrac{\partial ^2 \varphi }{\partial t^2} = 1 Initial Conditions: \varphi (x, 0) = 1; \varphi_t (x, 0) = 1 Boundary Condition: \varphi (0, t) = 1 On 0 \leq x < \infty, 0 \leq t < \infty...

Homework Statement Use the Laplace transform approach to find the renewal function for a renewal process with interrenewal p.d.f. as follows: g(x) = (c^2)xe^(-cx) , x > 0 The Attempt at a Solution M*(s) = G*(s)/(1-G*(s)) where M*(s) and G*(s) denote laplace transforms I have that G*(s) =...

Homework Statement y''-4y'+4y = 0 y(0)=1, y'(0)=1 Homework Equations The Attempt at a Solution This is annoying, because it feels very easy and I don't know why I am not getting the answer. Skipping the routine: s^2L{y} - s - 1 - 4sL{y} + 4 + 4L{y} = 0 (s+3) / (s^2 - 4s +...

Google seems to provide not much information on this. In essence, I am asking about the eigenfunctions of the Laplace transform when λ=1? Anyone have any insights on this rather unusual problem? BiP

Homework Statement Evaluate the laplace transform of {t2e7tsinh(3t)} Homework Equations Laplace transform of {tnf(t)}=(-1)ndn/ds2 * F(s) The Attempt at a Solution I've replaced it with (-1)2d2L{e7tsinh(3t)} I'm not sure how to proceed, though, as I don't really see how to take...

Hey all, Learning the Laplace transform and I get the point that it is a transformation but I would like to know what are some of the merits of the Laplace transform or more general why perform transformations in the first place. Any examples would be helpful.

y"-8y'+20y=tet, y(0)=0, y'(0)=0 I need to know if I made a mistake in getting to the step below: L-1{ 1/[(s-1)2(s2-8s+20)] } because when I solve that, I get something pretty gnarly..

I've been wondering whether the Laplace transform is injective. Suppose I have that \int^{∞}_{0}e^{-st}f(t)dt = \int^{∞}_{0}e^{-st}g(t)dt for all s for which both integrals converge. Then is it true that f(t) = g(t) ? If so, any hints on how I might prove it? Thanks! BiP

I'm not sure about the answers to parts of the limit step of the work. Can you explain what the answer to that step should be?

1. The limit as b approaches infinity always shows up as undefined on my calc so I don't know what to put for that section of the work. 2. What pat of the work is supposed to need L'hopital's rule? The integration?

Homework Statement I am trying to work out the inverse Laplace transform of t^2*u(t-a). Homework Equations The Attempt at a Solution I have been old that it starts (t-a)^2*u(t-a)... which I understand is substituting for (t-a). But I cannot seem to work out the rest can...

Homework Statement Find the inverse transform of the function F(s) = log\frac{s-2}{s+2} Homework Equations L(\frac{f(t)}{t}) = \int^{∞}_{s}F(x)dx f(t) = tL^{-1}(\int^{∞}_{s}F(x)dx) The Attempt at a Solution I missed the lecture on this and while I was able to figure out...

Homework Statement L-1{\frac{s}{s^2+4s+5}} Homework Equations \frac{s-a}{(s-a)^2+k^2} \frac{k}{(s-a)^2+k^2} The Attempt at a Solution I completed the square for the denominator and got: L-1{\frac{s}{(s+2)^2+1}} (a= -2, k=1) But how do I get rid of the s in the numerator? Or do I have...

Hey guys! I'm stuck on a Laplace transform. Following is the problematic function: [cos(t)]^3 Seems simple, but I'm having issues doing the Laplace transform on odd trigonometric functions. When I use the half-angle formula, I get this, which I can't seem to solve: 1/2cos(t) +...

Homework Statement I'm given the transfer function of LTI system is \frac{1}{s^2 + 4} Homework Equations H(s) = \frac{Y(s)}{X(s)} The Attempt at a Solution first of all I had to find diff. equations of the system. I found that it's y'' + 4*y = x; Then they asked to find such...