Laplace transform Definition and 779 Threads

How can I solve this Laplace transform (or how can I find series solution)? http://www.forkosh.dreamhost.com/mathtex.cgi?M=\int[/URL] _0^{\infty }e^{-\text{kR}}J_1^2(\text{ka})dk[/PLAIN] ;R>2a

Homework Statement ...find the inverse transform of the given function. F(s)= (2s+2)/(s2+4s+5) Homework Equations On another page, I see these 2: f(t)=eatsin(bt)--------->F(s)=b/[(s-a)2+b2) f(t)=eatcos(bt)--------->F(s)=(s-a)/[(s-a)2+b2) The Attempt at a Solution This is my first time...

Homework Statement y'' -6y' + 9y = f(t) f(t)= 0, 0<t<1 1, 1<t<3 0, t>3 Homework Equations The Attempt at a Solution Turning it to heaviside functions I get: y'' -6y' + 9y = u1 - u3 and I solve. in the answers it should be: y(t) = 2tet + u1(1/9 - 1/9e3(t-1)+...

Laplace Transform of unit step function HELP! Homework Statement f(t)= e^t on 0<=t<1 . . . . t on 1<=t<2 . . . . sin(t) on 2<=t<infinity Homework Equations Unit Step Function The Attempt at a Solution Here is my attempt at a solution...

I'm trying to use the Laplace transform to work out another capacitor problem, the voltage as a function of time on a capacitor that's discharging into another capacitor through a resistor. It's the classic two capacitor problem, but I'd like to actually find an expression for the voltage as a...

Homework Statement I'm trying to use the Laplace transform to find the charging equation of a capacitor with an initial voltage already on the capacitor.Homework Equations V_i = RC\frac{dVc}{dt} + V_c The initial condition of Vc will be \lambda. The Attempt at a Solution V_i(s) = sRC*V_c(s)...

Homework Statement Given: \frac{d^2y}{dt^2} + 12\frac{dy}{dt} + 32y = 32u(t) and that all initial conditions are zero, use the Laplace transform to find y(t) This is an example problem from my text. They start the solution by taking the Laplace of both sides assuing y'(0) = 0 & y(0)...

ok I am given the problem ((s/s^2+4)+s+5))/(s^2+6s+18) I use the expand function of my ti-89 and get ((163/70)*s)/((s+3)^2+9) + ((398/85))/((s+3)^2+9) + ((7/170)*s)/(s^2+4) + (6/85)/(s^2+4) 1st term--------------------2nd term-----------------3rd term-------------4th term ok my...

Homework Statement t y'' + (3 t-1) y' + 3 y = 6 e^{-3t} y(0) = 1 y(5) = 2 Homework Equations The Attempt at a Solution I tried applying the Laplace transform to the equation but I was having a little trouble... L [t·y''] = -dL[y'']/ds = s2·Y' + 2·s·Y - y(0) = s2·Y' + 2·s·Y - 1 L...

I am asked to find inverse laplace of (3s+5)/(s^2-6s+25) I do partial frac and get (3s)/((s-3)^2+16) + (5/(s-3)^2+16) I do the translation and get [(3s)/s^2+16 + 5/(s^2+16)]*e^3t My final answer is e^3t[3cos(4t) + 5/4sin(4t)] but the book says the sin term should be 7/2sin(4t)? I say...

Homework Statement Could \[F(s) = \frac{1}{{s(1 - {e^{ - s}})}}\] be the Laplace transform of some periodic function? Why? If so, find that periodic function The Attempt at a Solution If it was the Laplace transform of some periodic function, the the Laplace transform of the first wave...

Homework Statement If f(t) transforms into F(s), so that \[ F(s) = \frac{{s + 1}}{{s^2 + as + 1}},a \in \] , prove that if a < 0, the function f(t) isn't bounded, and if a >= 0, it is bounded. Prove that if -2 < a < 2, f(t) oscilates. The Attempt at a Solution I honestly have...

Homework Statement Find the Laplace transform for \[t\left( {\int\limits_0^{t - a} {f(u)du} } \right)H(t - a)\] proving the properties used. Homework Equations If f(t) transforms into F(s): a) \[{( - t)^{n}f(t) \to {F^{(n)}}(s)\] b) \[\int\limits_0^t {f(u)du} \to...

I have this DE: \[y'' - 4y' + 8y = f(t) = \left\{ \begin{array}{l} t{\rm{ }},t \in [0,2) \\ t + 1{\rm{ }},t \in [2,4) \\ 0{\rm{ }},t \ge 4 \\ \end{array} \right.\] I have problems transforming f(t). I know that when I have a function defined by parts, I...

Hello, I am trying to take the Laplace transform of floor(f(t)) in order to solve the differential equation f'(t)=floor(f(t)). I know that http://functions.wolfram.com/IntegerFunctions/Floor/22/04/" gives L(floor(t)) = (e^(-s))/(s(1-e^(-s))) instead -- are these equivalent?) and L(f(t)) =...

Hello, I am trying to take the Laplace transform of floor(f(t)) in order to solve the differential equation f'=floor(f(t)). I know that L(floor(t)) = (e^(-s))/(s(1-e^(-s))) and that L(f(t)) = F(t) (of course), but I realized that I have no idea how to take the Laplace transform of a...

Hi, I want to inverse this laplace transform, -(s^(1/2)), seems that the inverse is in complex plane. Where should i start to find this inverse... Thank you.

"easy" Laplace Transform...help! Homework Statement Evaluate L{(e^-2t)*t*sinht} Homework Equations translation theorem The Attempt at a Solution Just to clarify: the contents of the bracket is the product of 3 terms: e^-2t (e to the power of -2t) t sinht all...

Homework Statement The solution to the ODE y''(t) + 4y(t) = 1 + u(t − 2), y(0) = 0, y'(0) = 0 is given by... The Attempt at a Solution OK well I figured this one is good to solve with Laplace transforms. So I took the Laplace of both sides to obtain (s2 + 4)Y(s) = [e-2s/s] + 1/s, which...

"Generalized" Laplace transform Hello, I'm having trouble proving injectivity of what might be called a "generalized" Laplace transform (not the one by Varma). Let f be a rational function and C be a fixed closed contour in the complex plane, (such that C contains not pole of f): The operator...

Homework Statement Find the inverse Laplace Transform of (9s+5)/(s2-9) given s>3 Homework Equations I have a table of Laplace Transforms. it says "sinh at" goes with a/(s2-a2) and "cosh at" goes with s/(s2-a2) The Attempt at a Solution I know how to split it up and find the...

Homework Statement Find the Laplace Transform of: f(t) = {0, t < 5 t2 - 10t + 31, t\geq5Homework Equations The Attempt at a Solution The answer I got was: F(s) = e-5s (2/s3 + 6/s) Is this correct?

Homework Statement Use the Laplace transform to solve the following initial value problem: x' = 7 x + 5 y, y'= -2 x + e5t, x(0)=0, y(0)=0 Find the expressions you obtain by taking the Laplace transform of both differential equations and solving for Y(s) and X(s) Homework Equations...

Homework Statement Find the Laplace transform of L{texp(9t)sin(2t)} Homework Equations (-1)^n F^n (s) The Attempt at a Solution I am not sure how to start it. The exp(9t) term throws me off. Usually I would just do (-1) F'(s) where F(s) is the laplace of sin(2t). But do I take...

Homework Statement supposed to prove informally that f(x)=Integral 0-->infinity (cosxt/(t^2+1))dt == Pi/2*Exp[-x] Homework Equations The Attempt at a Solution no clue, need some hints to get started

Homework Statement Find the Laplace transform of f(t). f(t) = -9t + 7 + u5(-7 + 9t + et) Homework Equations The Attempt at a Solution The Laplace transform of -9t is just -9/t2 The Laplace transform of 7 is 7/s But I am not sure how to find it for u5(-7 + 9t + et). In the...

I have some problems where I am to take the Laplace transform of some functions, for example te^{xt} not by using the integral definition but instead by using a table of transforms and the fact that the Laplace transform is a linear operator. However, the instructions say that "A preliminary...

Homework Statement Determine the inverse Laplace transform of the given function F(s) = (2s+1) / (s^2 + 16 ) Homework Equations the LaPlace transform of different functions The Attempt at a Solution I divide the above equation into 2 fractions one with the 2s in the numerator...

Homework Statement find laplace transform of F(s)= (1/t)*(exp(2t)-1) Homework Equations stated answer: ln(s/(s-2)) The Attempt at a Solution i really don't know where to start with laplace. my teacher has done a terrible job really jusut explaining the simplr process. Should i...

Explain why the functions F(s)=\frac{s^2+4s+17}{s^5+16s^3+2^2+6} G(s)=\frac{2s}{(s^2+4)(\sqrt{1+s^2})} are Laplace transforms. (DO NOT TRY TO INVERT THESE LAPLACE TRANSFORMS) Is it something to do with some basic property of laplace transform?

L^{-1}(\frac{1}{\sqrt{1+s^2}})=?

Homework Statement http://u1.imgupload.co.uk/1257811200/9e4e_image.bmpHomework Equations find aboveThe Attempt at a Solution in fact i had no problem in the progress of doing this question and finally i got F(s)= 1/1+s^2 and i want to ask it is vaild for all value of s since it is s^2? is it...

Hi, We know that if a function does not have a Fourier transform, then it does not have finite energy. Is there an equivalent intuition associated with a function that does not have a Laplace transform?

I have the correct solution of this problem (cos(t)+u_{3\pi}[1-cos(t-3\pi)]). As you can tell from my solution below I am off by a extra negative sign on the cos(t) coefficient. I have had this same issue on several other problems, so I believe I must be missing something on the procedure. Any...

Homework Statement This is my first post, so bear with me. I have seen others who have posted their questions and the problem looked like it was typed in mathcad or something. How do I do that? Ok so I'm trying to figure out how to solve a piecewise Laplace transform when f(t)=t the...

Hello, By definition, the forward Laplace transform of a function f(x) is: \mathcal{L}\left\{f(x)\right\}=\int_0^{\infty}\text{e}^{-sx}f(x)\,dx. Can we say the same for the function f\left(\frac{1}{x}\right), i.e...

Homework Statement Solve: ty''+2y'+y=tJ₂(2√t) with y(0)=y'(0)=0 Homework Equations The Attempt at a Solution Applying the laplace transform i get: L(y)=Y L(2y')=2sY L(ty'')=-2sY-s^2Y Putting this together: -2sY+2sY+Y-s^2(dy/ds)=[e^-(1/s)]/s^3...

Homework Statement hi guys, i need to find the inverse Laplace transform of s/((s+1)^(2) +4) the acual question is an IVP, i have worked trough it and am just about finished but i am stuck on this transform. how would you go about getting this into a form that can be transformed like...

Homework Statement Using Laplace transform to solve 4th order DE with a delta dirac forcing function. Has a tricky denominator, I just need a clue. y^{(4)} - y = \delta (t-2) __ IV's y'''(0)=0 , y''(0)=0 , y'(0)=0 , y(0) = 0 Homework Equations I am asked to convert the solution...

Homework Statement A 2nd order DE with a Delta Dirac forcing function, I have been asked to solve in my DE course. y'' + 2y' + 10y = \delta(t-1) Also given are IV's y'(0)=0, y(0)=0 Homework Equations At this stage in my course I am being asked to only use the method of partial...

I'm trying to find the laplace transform (if possible) of exp(-2r/a)r^2. --- I did integration by parts to check that the integral of exp(-2r/a)r^2 from 0 to infinity is a^3 / 4. but i cannot get the laplace transform to work out. the answer mathematica online gives would have to have the term...

Homework Statement Help, I don't know how to do the following question: Using Laplace to solve x' -y =1 2x' +x +y' = (t2-2t+1)e-(t-1) Homework Equations x(1)=0 y(3)=0 The Attempt at a Solution The problem I'm having is the initial conditions aren't at zero, and I'm not sure...

Homework Statement Find the inverse laplace transform of In(1+1/s) Homework Equations The Attempt at a Solution Using the complex inversion theorm, and the sum of the residues. The only residue is at s=0. and it is a simple pole of degree one. Therefore lim(s approaches...

Homework Statement \int_{\pi/2}^{\infty}cos(t)e^{-st}dt Homework Equations \int vdu=uv-\int udv v=cos(t) , dv=-sin(t)dt , du=e^{-st} , u=\frac{-e^{-st}} {s} The Attempt at a Solution \int_{\pi/2}^{\infty}cos(t)e^{-st}dt = \frac{-e^{-st}}{s}cos(t) -\int...

Homework Statement get laplace transform of sin(4t+5) Homework Equations using some trig identity i.e. Sin(a+b)=sin(a)cos(b)+cos(a)sin(b) or any other that could simplify it The Attempt at a Solution applying the trig identity =sin(4t)cos(5)+cos(4t)sin(5) taking the transform...

I've been trying to understand what the Laplace Transform means via It's definition. Even if you are trying to evaluate a simple exponential function:F(s) = \mathcal{L} \left\{f(t)\right\}=\int_0^{\infty} e^{-st} f(t) \,dt. it will not converge for all S in a Riemann sense. I've been trying...

According go Wikipedia the inverse Laplace Transform is given by: \mathcal{L}^{-1} \{F(s)\} = f(t) = \frac{1}{2\pi i}\lim_{T\to\infty}\int_{\gamma-iT}^{\gamma+iT}e^{st}F(s)\,ds, How do you probe this? I'm surprised that it doesn't depend on the value of \gama...

I was exploring the connection between the Laplace transform and the Fourier transform (see "=http://earthcubed.wordpress.com/2009/08/30/using-the-fft-to-calculate-the-laplace-transform/"[/URL])and it occurred to me that the from the definition of the Laplace transform: F(s) = \mathcal{L}...

My books aren't clear at running through these inverse laplace transforms and this ones got me snookered. I'm trying to perform the laplace transform of: 1/s + 40/(24s^2 + 40s + 40) Factor out 24 becomes 1/s + 1.667/(s^2 +1.667s +1.667) Finding A, B, C A/s + Bs+C/(s^2 +1.667s...

Hello! I am trying to solve a PDE for it's Green function, I found myself in a position to know G(is) where "i" is imaginary unit, G(s) is a Laplace transform of g(t) and g(t) is the Green's function I am after. So, I've been snooping around and found Mellin's inverse formula at...