Laplace Definition and 1000 Threads

This is some homework from my Analog Signal Processing class, it's a cool class and I've not had much trouble, but this is giving me a bit of a problem and I was hoping someone could help me see what I'm doing... Here's the problem: Sketch, Get the Laplace Transform of, and Sketch the complex...

Homework Statement Solve df/dx (x)+ f(x)= 3 under the condition f(0)= -2 using the Laplace transformations Homework Equations The Attempt at a Solution Not even sure where to start on this one. Dont have any examples that point me in the right direction. Any ideas anyone??

Hello Everybody. I gave a quick look onto the internet but i couldn't get anything interesting. Heres my problem. Im solving the differential equation given by: (-\Delta+k^2)^2u=\delta Where \delta is the dirac delta distribuiton (and u is thought as a distribution as well) The...

Solve the following given y(0) = 0 & y'(0)=1: y′′+3y′+2y = u2(t), such that u2(t) is a heaviside step function Here's what I've got so far, =>s2Y(s)−sy(0)−y′(0) + 3sY(s)−3y(0) + 2Y(s)= exp(−2s)/s Y(s) = (exp(−2s) + s) / (s(s2+3s+2)) Y(s) = exp(−2s)/(s(s2+3s+2))* + 1/(s2+3s+2)** The...

Homework Statement y(x) = e^{3x} + \int_0^{x}\hspace{1mm}y(t)\hspace{1mm}e^{x-t}\hspace{1mm}dt Homework Equations (f*g)(x) = \int_0^{x}\hspace{1mm}y(t)\hspace{1mm}g(x-t)\hspace{1mm}dt L(f*g;s) = L(f;s)L(g;s) I will use Y(s) to denote L(y;s) The Attempt at a Solution I tried...

I'm trying to solve the homogeneous heat equation of a semi-infinite cylinder in cylindrical coordinates for a semi-infinite cable (no theta dependence): \frac{\partial U}{\partial t}=D\left(\frac{\partial^{2} U}{\partial r^{2}}+\frac{1}{r}\frac{\partial U}{\partial r}+\frac{\partial^{2}...

I read through that 800 something page Dover book on differential equations, but I feel like I haven't had enough practice. I need several problems and solutions, but mostly Laplace transform problems. In fact even just Laplace transform problems would be greatly appreciated.

Homework Statement Derive the second order differential equation relating x(t) and y(t). Using the Laplace transform, find the total response as a function of the zero input response and the zero state response in the following form.Homework Equations Y(s)=Yzs(s) + Yzi(s) The Attempt at a...

Hi, I was wondering what the prerequisites are for doing Laplace Transforms. I'm just a little confused with one of the examples : \int_0^{\infty} = e^{-sx} dx = [e^{-sx}/s]_0^{\infty} = 1/s I understand that e^{-s(0)} is 1. But where does the e^{-s(\infty)} part go? Is there something I...

Homework Statement Okay, I'm pretty lost in my differential equations class and I'm not sure how to transform the functions Homework Equations f(t)= 1 / (s+2)^2 f(t)= 1 / (s+3)^3 f(t)= 1 / (s^2-3^2) They seem pretty simple, but i have no clue if whether I'm suppose to use 2 formulas or...

After solving a simple circuit with a inductor L in series with resistor R Driven by Voltage source V0 by using Laplace Transform we get I(s) = \frac{V}{s (R + Ls} Why do we call this the frequency Domain response? What does 's' represents?

Homework Statement Given a transfer function in the Laplace Domain Detemine an expression for x(t), given f(t) is a sinusodial input with frequency omega = root(k2/m2) and amplitude of 1 N (initial conditions equal 0)Homework Equations...

Laplace Transform of... Few months back my friend called me to help him (and his whole class!) finding the Laplace Transform of \sin \sqrt{t}. Since then I found myself wasting hours and days (even before non-mathematics exams!) trying to solve the problem. I also checked the provided answer...

Homework Statement \mathcal{L}\left[\frac{\sin(t)}{t}\right]=? Homework Equations \mathcal{L}\left[f(t)\right]=\int_0^\infty e^{-zt}f(t)dt The Attempt at a Solution \int_0^\infty e^{-zt}\frac{\sin(t)}{t}dt=\int_0^\infty \frac{e^{-zt}}{t}\left(\frac{e^{it}-e^{-it}}{2i}\right )dt...

F(s) = \frac{1}{K^s} where K is a positive real.

Homework Statement solve the differential equation by using Laplace transform x^{''}(t)+7x^{'}(t)+10x(t)=sin3t x(0)=0, x^{'}(0)=0 Homework Equations X(s)s^2+X(s)7s+X(s)10=\frac{3}{s^2+9} then i get X(s) = \frac{3}{s^2+9}\cdot\frac{1}{(s+5)(s+2)}...

Hi, so we just started learning about Laplace transforms yesterday, and I have a problem which I am not sure what to do: My question is about the second term, if it was a constant coefficient I could do this fine, but none of the 2 examples we did in class for solving ODEs with Laplace...

Homework Statement Find the Laplace transform of the given function, a and b are real constants. Hint: cos(bt)=(e^ibt+e^-ibt)/2 and sin(bt)=(e^it-e^ibt)/2i. f(t)=e^(at)*sin(bt) The attempt at a solution The LaPlace transform of e^at is 1/(s-a). The LaPlace transform of sin(bt) is...

Hi all Conventionally we used to seeing the Laplace transform applied to problems that use time as the independent variable, can anybody point me at some examples that do not use time as the independent variable? Thanks Tim

Homework Statement I'm trying to solve a definite Laplace transform. The function is defined as f(t) = sin(t) over the interval [0, \pi] Homework Equations The integrate to evaluate is: \int_0^\pi e^{-st} sin(t) dt The Attempt at a Solution To evaluate, first use integration by...

Homework Statement So I finally had my final today, and I was so worried because I needed a 90% at least to pass the class with an A. :\ So I'm really worried with a few of my answers. One of those (that I can remember) was the laplace transform of: t(sinh(3t). Homework Equations laplace t...

Homework Statement 2y'' + y' + 4y = ∂(t-π/6)sin(t); y(0)=0, y'(0)=1/2. Homework Equations Dunno The Attempt at a Solution The left side of the equation is what's tripping me up. There's nothing on my Elementary Laplace Transforms table that has the Dirac delta function...

Homework Statement Find the Laplace transform of each of the following functions: ... 2. f(t)=eatcos(bt) 3. f(t)=tn, were n is a positive integer Homework Equations As you well know, taking the Laplace of f(t) means ∫f(t)e-stdt from 0 to ∞ The Attempt at a Solution...

Hello, I am trying to find the laplace transform of \frac{f(t)}{t} http://nptel.iitm.ac.in/courses/Webcourse-contents/IIT-KANPUR/mathematics-2/node92.html Lemma 10.3.9 I don't understand why we are taking the limit as s goes to infinity Can anyone help me? thank you

Just out of curiosity, I've been looking into the Laplace transform and noticed that... \mathcal{L}(sin(t))=\frac{1}{s^2+1}=\frac{d}{ds}(tan^{-1}(s)) So, I was wondering if the Laplace transform of the sinc function was the inverse tangent function. In LaTEX...

Homework Statement I have a couple of problems that I am stuck on. The following: y'' - 6y' + 9y = t y(0) = 0 y'(0) = 1 and y'' - 6y' + 13y = 0 y(0) = 0 y'(0) = -3 Homework Equations y'' = s2Y(s) - sf(0) - f'(0) y' = sY(s) - f(0) y = Y(s) The Attempt at a Solution...

I'm deriving the heat equation using Laplace transforms. I'm up to u(bar) = Aesqrt(s)x + Be-sqrt(s)x. My boundary conditions are lim(x tends to 0) = 0 & this makes A = 0, so u(bar) = Be-sqrt(s)x My other BC is ux(0,t) = -Q My question is how do I get B using this BC? I tried using the def...

Homework Statement the inverse laplace transform of ln\frac{s+2}{s-5} using the inverse Laplace transform of the derivative Homework EquationsL^{-1}{\frac{d^{n}}{ds^{n}}F(S)} = (-1)^{n}t^{n}f(t) The Attempt at a Solution the integral of ln\frac{s+2}{s-5} I worked to be (s+2)ln(s+2)-(s+2)...

Homework Statement http://img710.imageshack.us/img710/3381/38442384.jpg The Attempt at a Solution [PLAIN][PLAIN]http://img695.imageshack.us/img695/6295/56987528.jpg Thanks in advance, JJ

Find the laplace transform {\cal L} (1 + t) Without using the table. im really having a hard time working these out please help!

Compute L[(t-3)u2(t) - (t-2)u3(t)] I come up with using unit step function but I don't know how to solve it

Homework Statement L{tcos(t)} Homework Equations Using the laplace transform find the equation. The Attempt at a Solution I already have a really long answer. . .I was just wondering if someone can explain this: Another method (appart from using integration by parts...

one of the questions my diff eq teacher gave us is L{(t^3)(sin^3(t))} (laplace of t cubed sine cubed t) i'll just cut to the chase and ask, would you be of the opinion that a question like this is in the scope of an intro to ODE class?

Homework Statement Solve the system of first order differential equations using Laplace Transforms: dx/dt = x - 4y dy/dt = x + y, subject to the initial conditions x(0)=3 and y(0)=-4. Homework Equations So far I've used the limited knowledge of Laplace Transforms for first order...

Homework Statement Solve using the Laplace Transforms (can not use partial fractions) f '(t) + \int2f(u) du = 2 + 3f(t) Homework Equations Using Laplace f '(t) gets replaced with sF(s) -f(0) \int2f(u) du gets replaced with \frac{2F(s)}{s} Please correct me if I'm wrong on...

Homework Statement \frac{s}{(s-a)(s-b)} Homework Equations Now I know that it results in: [tex]\frac{ae^(at)-be^(bt)}{a-b}[\tex] The Attempt at a Solution OK, I don't have the slightest clue where to begin. Could someone point me in the right direction? I've looked at all...

Homework Statement y'' + ty' - y = 0 plugging in the known Laplace formuals i get this... [s^2Y(s) - sy(0) - y'(0)] + [-sY'(s) - Y(s)] - Y(s) = 0 Homework Equations y(0) = 0 y'(0) = 3 The Attempt at a Solution simplying to a linear first order DE -sY'(s) + (s^2-2)Y(s) = 3...

Homework Statement Let f(t) denote a causal signal. Show that L+ {f(−at)} = 0 for any a > 0. Homework Equations The Attempt at a Solution I know that the laplace{f(at)} = 1/a*F(s/a) but by simply placing -a whenever determining the Laplace, my signs gets confused within the...

Homework Statement Find the Laplace transform of cos(t)h(t) if the LT of h(t) (unit step) is 1/s Homework Equations --- The Attempt at a Solution Since the unit step isn't shifting anything anywhere, can I just treat it as 1? Seems too simple, haha. Any ideas? thanks.

Homework Statement I need to solve the Laplace equation, u_rr + (1/r)u_r + (1/r^2)u_{theta}{theta} = 0, on a circular wedge with radius R, angle {alpha}, where u(r,0) = 0, u(R,{theta}) = 0, and u(r,{alpha}) = 50. Homework Equations The Attempt at a Solution Separate variables -...

Homework Statement The steady state temperature distribution, T(x,y), in a flat metal sheet obeys the partial differential equation: \frac{\partial^2{T}}{\partial{x}^2}+{\frac{\partial^2{T}}{\partial{y}^2}}=0 Separate the variables and find T everywhere on a square flat plate of sides S with...

When trying to solve a pde using Laplace transform, I need to invert an expression of the form \frac{\exp{(-as-b\sqrt{s})}}{s^2} A friend told me that Mathematica cannot invert such expression. I try using convolution but a bit loss when trying to evaluate the integral of Erfc(.)...

Homework Statement Find the unit impulse response for the operator D^4 + I, using the Laplace transform. Homework Equations The Attempt at a Solution w^(4) + w = δ(t) s^4W + W = 1 W = 1 / (s^4 +1) Now, I need to find the inverse laplace transform of W. But I don't know how to simplify W...

Homework Statement It's been a while since I've done laplace transforms, but I need some help with one! I am supposed to find the laplace tranform for the following signal. This is for my circuits class btw. xa(t) = 2u(t-1) Homework Equations Laplace tables...

Homework Statement Simply find L{Sin(bt)}Homework Equations My Professor gave us a hint "Use Integration by Parts TWICE" The Attempt at a Solution so i start with the usual limit as N -> infinity the integral of e^(-st)sin(bt)dt Integrating by parts i get ( u = sin(bt) du = bcos(bt) dv =...

Homework Statement Using laplace transform, solve: y'' - y = \frac{x^2-3x+2}{|x^2-3x+2|} y(0)=y'(0)=0 Homework Equations The Attempt at a Solution Just to know if I'm on the right path - Since the quadratic has 2 roots, at 1 and at 2, the entire thing can be equal to...

Homework Statement Not a homework problem exactly, but in an EE textbook I saw something to the following effect: To obtain the time domain behavior for \frac{s}{s^2+\frac{\omega_0}{Q} + {\omega_0}^2} the following Laplace transforms are combined to cancel the term in the numerator...

Homework Statement Need to find the Laplace transform of |sint| (modulus). Homework Equations The Attempt at a Solution I am really not sure how to proceed here - any help would be much appreciated.

Homework Statement I'm supposed to find the inverse Laplace transformation of the following equation Homework Equations G(s) = s+1/s2+25 The Attempt at a Solution I was thinking of using one of the shifting theorems because I know that L-1 {1/s2+25} is just sin(5t) but I don't know how to...

Homework Statement I need to find the inverse Laplace transform of s/(s^2+a^2), where a is a constant, by the method of residues. I need to prove the part of the contour not actually relating to the desired integral tends to zero as R---> infinity. Homework Equations The...