Laplace transform Definition and 752 Threads

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?

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 \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 was trying to prove that the Laplace transform is unique and was wondering if anyone could tell me if I've made any errors in my attempt. Here it is: Suppose L(f) = L(g), where L() denotes the Laplace transform. We want to show that f = g. By linearity of the transform, L(f - g) = 0...

Homework Statement Use the Laplace Transform to solve: y"+2y'+2y=t y(0)=y'(0)=1Homework Equations L{y(t)} = Y(s) L{y'(t)} = sY(s)-y(s) L{y"(t)} = s2Y(s)-sy(0)-y'(0) using the laplace transform table: tn = n!/(sn+1) where n=1The Attempt at a Solution Take laplace on both sides: L{y"(t)} +...

Homework Statement t*e^(it) how do we take the laplace transform of this . would it be 1/((s-i)^2) then how would we get the real part of that .

Hello, if i said that x(t) is real, why X(s) must occur in conjugate reciprocal pairs ?

I'm reading a paper on tissue cell rheology ("Viscoelasticity of the human red blood cell") that models the creep compliance of the cell (in the s-domain) as J(s) = \frac{1}{As+Bs^{a+1}} where 0\leq a\leq 1. Since there's no closed-form inverse Laplace transform for this expression, they...

Homework Statement Find the Laplace Transform of the given function H(t-1)t^2 I'm not sure how to add (t-1) to the t^2 term to solve the problem Any help would be greatly appreciated.

Homework Statement find the transform of sin (wt) u(t - b) I have to get it into the form for the time shift but I do not know how to deal with the unit function help appreciated

Homework Statement Find the solution of the given initial value problem: y''+4y=upi(t)-u3pi(t) y(0)=7, y'(0)=5 The Attempt at a Solution So I found the L{} of the above equation: s2Y-s*f(0)-f'(0)+4Y = (e-pi*s)/s-(e-3pi*s)/s Combining and substituting the numbers I get...

Homework Statement s2-5 / s3+4s2+3s Homework Equations find the inverse laplace transform The Attempt at a Solution for the denominator, it can be factored out to s(s+3)(s+1) or one could complete the square and thus the denominator would be s(s+2)2-1. neither of this help in...

I am reading a text about Laplace transform in solving differential equations. Seems that this method is so powerful. To practice how it works, I makeup a very simple problem \frac{dy}{dt} = e^{wt}y This equation could be solved by variable separation and then intergrate LHS and RHS. But I...

to calculate the inverse laplace transform of a function F(s), s+2 was replaced with z for convenience. the inverse laplace transform of z was found--let's denote the function g(t). now, how do i prove that L-1{F(s)} = L-1{F(z-2)} = g(t) * e-2t i am attempting to prove by rewriting...

Homework Statement I need to find the laplace transform of f(t)=tcos(t). Homework Equations \int e^-^s^ttcos(t)dt The Attempt at a Solution I just need help on how to integrate this. I can find the answer easily using the f(t)=tcos(kt) general formula but I wish to find it directly.

Homework Statement Use the Laplace Transform to solve the PDE for u(x,t) with x>0 and t>0: x(du/dx) + du/dt = xt with IC: u(x,0) = 0 and BC: u(0,t) = 0 Homework Equations The Attempt at a Solution After taking LT of the PDE wrt t, the PDE becomes x(dU/dx) + sU = x/(s2)...

Homework Statement The problem is not getting the answer to the laplace transform but instead reducing my answer so i dnt lose marks. If i work out the laplace transform of: L(t^3 * sinh(4t)) to be 3!/(2(s- 4)^4)- 3!/(s(s+ 4)^4) then how do i add these to get a single fraction? Its doing...

L-1(1/(s+2)3) I don't see this one in the table. How do I solve the inverse Laplace transform? I know from class notes that the answer is (1/2) t2e-2t But I don't know to get it. Thanks!

I need to find the laplace transform of y''(t)-y(t)=0 with initial conditions y(0)=1 and y'(0)=3 My attempt: Ly''(t)=(s^2)F(s)-s(1)-(3) Ly'(t)=sF(s)-1 so (s^2)F(s)-s(1)-(3)-sF(s)-1=0 I need to isolate F(s) so F(s)=-(2/s^2) Is this correct?

http://users.on.net/~rohanlal/laplacetrans5.jpg In the third line, what is S+4 the laplace transform of?

Hello, I know normally giving solutions is frowned upon, but I have lost my colleagues data sheets and desperately need this transform to continue my work. I am looking for the Inverse Laplace Transform of the Transfer Function: H(s) = 1 / (s^2 + 20s + 5K) where K is an as yet unknown...

Okay so this problem has been giving me nightmares ever since I laid eyes on it. The problem: y'' - y = f(t), y(0) = 1, y'(0) = 0 f(t) = 1, 0 (less than equal to) t (less than) pi/2 f(t) = sin(t), t (greater than equal to) pi/2 Any help would...