Laplace transform Definition and 779 Threads

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 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 Hi all. I have found the Laplace transform of the following piecewise function: f(x) = \left\{ {\begin{array}{*{20}c} {0\,\,\,\,{\rm{for}}\,\,\,\,x < 0} \\ {x\,\,\,\,{\rm{for}}\,\,x \in (0;1)} \\ {0\,\,\,\,{\rm{for}}\,\,\,\,x > 1} \\ \end{array}} \right. I...

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...

1) If Laplace transform...Cos(3t) = s/(s^2+9) but how about laplace transform ...Cos(3) = ? 2) Cos(0) =1 but how about Cosh(0) =? ; Cosh(1) =? Sinh(0) = ?; Sinh(1) = ? 3) How to do the partial fractions for ... (s+13)/(s^2 +2s+10) = ?? Thx for help =)

Homework Statement Find the Laplace transform of the pendulum equation. Homework Equations The pendulum equation: \frac{d^{2}\theta}{dt^{2}} + \alpha \frac{d \theta}{dt} + g \sin(\theta) = 0 s = \sigma + i \omega The Attempt at a Solution Taking the laplace transform I get...

Homework Statement Find the laplace transform of the following: (1-3cost)/t^2 Homework Equations The Attempt at a Solution I know many methods to find the laplace transform like the first and second shift theorems, the differentiation one, convolution, but for this particular...

I'm having some trouble getting the inverse Laplace to the following problems...I need some help F(s)=24/s^5 F(s)= 4/[((s-2)^2)+25 F(s)= s/(s-1)(s+1)

Homework Statement The problem just states to find the Laplace Transform of cos(kt) from its power series expansion, instead of using the formula for the transform of a periodic function.Homework Equations Equation for Laplace transform of a function f(t) ->\int(e^{-st}f(t))dt Power Series...

Homework Statement (1 pt) Given that L(cos(5t)/(pi*t)^.5)=exp(-5/s)/sqrt(s) find the Laplace transform of . sqrt(t/pi)cos(5t) Homework Equations I honestly have no idea. There is the integral of f(t)exp(-st) though The Attempt at a Solution Ive tried many reasonings...

Homework Statement I'm a little a bit confused about the following exercise because of the two segments of the function. How can we find the Laplace transform of this function f(t) = \begin {cases} t , 0\le t < 4 \\ 5 , t\ge 4\end {cases} Homework Equations The Attempt at a...

Homework Statement Show that f(t)=e^(5t) sin(t) satisfies the condition for the LaPlace transform to exist I can solve the Laplace and get 2/((s-5)^2 + 4) How do I show that the conditions exist? If it is solvable using the table, shouldn't that be enough?

Homework Statement Find f(t). Homework Equations L^{-1}\left\{\frac{s}{s^{2}+4s+5}\right\} The Attempt at a Solution I tried completing the square to get to the solution and I ended up with: L^{-1}\left\{\frac{s}{s^{2}+4s+5}\right\} =...

Homework Statement Find the Laplace transform of f(t) = sin(2t)cos(2t) using a trig identity. Homework Equations N/A. The Attempt at a Solution I know the double-angle formula sin(2t) = 2sin(t)cos(t) but that's not helping much. Can you give me some advice on how to...

Homework Statement Where to begin when trying to calculate the inverse Laplace transform of \hat{f}(s)=\frac{1}{\sqrt{s+1}}? I know it's tabulated, but I'd like to calculate it without resorting to a tabulated result. Thanks

Homework Statement y''+y = f(t) y(0) = 0; y'(0)=1 f(t) = 1, 0<=t<pi/2 0, pi/2<=t The Attempt at a Solution so far, i have (s^2+1)*L{y} = \frac{s-e^(-pi/2s)}{s} +1 what is next ?

Homework Statement This is a problem from my book that I'm very close to finding the solution to, but I'm a little off. I have a feeling it's some small error I'm just overlooking because I'm so hungry/sleep-deprived. Anyway, the question asks you to find the Laplace transform of the given...

Homework Statement This isn't a homework, I'm just trying to recap for a mid-term. Anyways, it's about inverse Laplace transformation and this crap is starting to piss me off! How the heck are you supposed to go from \frac{ \frac{-U}{s}}{R+sL+ \frac{1}{sC}} to - \frac{2 \sqrt{10}}{...

How do I do the inverse of this? 1/(s+a)n is not in the table. \begin{array}{l} Y\left( s \right) = \frac{1}{{\left( {s + 4} \right)^4 }} \\ y\left( t \right) = L^{ - 1} \left[ {Y\left( s \right)} \right] \\ \end{array}

From the class notes: \begin{array}{l} y'' + 8y' + 16y = te^{ - 4t} ,\,\,\,\,\,y\left( 0 \right) = y'\left( 0 \right) = 0 \\ \\ L\left[ {y''} \right] + 8L\left[ {y'} \right] + 16L\left[ y \right] = \frac{1}{{\left( {s + 4} \right)^2 }} \\ \end{array} How did he get...

Homework Statement L{sinh(bt)} Homework Equations sinh(bt)=(e^bt-e^-bt) The Attempt at a Solution so the answer says it's b/(s^2-b^2) but get get that far.. here's what i have ... 1/2L{e^bt}+1/2L{e^-bt} = 1/2[e^((s-b)t)-e^((s+b)t)]

The question: Find the Laplace transform of f(t)=te^2^t I have got: Though, this will not become f(s) = 1/(s+2)^2 Anyone got an idea about what I am doing wrong?

Homework Statement What is the Laplace transform of f(t) = 0 for 0 < t < 2 and f(t) = (4-t) for 2 < t < 3 and f(t) = 1 for 3 < t < 4 and f(t) = (5-t) for 4 < t < 5 and f(t) = 0 for t > 5? Homework Equations The Attempt at a Solution f(t) = H(t-2)(4-t) - H(t-3)(4-t) + H(t-3) - H(t-4) +...

this isn't homework, this is just general knowledge and i can't figure it out.. please help, thx Find the Laplace transform of the given function: f(t) = { 0 t<2, (t-2)^2 t>=2 I tried working it out and this is where i get stuck f(t) = (t-2)^2 * u(t-2) I am not sure if I got the...

Hello from Greece!Gongrats for your forum. I was wondering if anyone could give me a hand with this initial value problem. It s to be solved via Laplace transform. y''(x)-xy'(x)+y(x)=5 , y(0)=5 and y'(0)=3 Applying the transform to the given equation I end up to ...

Hello, I'm trying to find some information concerning Laplace transforms. Are they "just" an integral transformation, or do they have some algebraic meaning similar to Fourier transforms (the "plane wave" basis vectors)? Thanks!

There are lots of tables out there for finding the inverse laplace transform of: \frac{1}{(s+b)^{2}+a^{2}} or \frac{s}{(s+b)^{2}+a^{2}} but what if a^{2} is negative? I don't know what useful formula I should split it up into.

Hey guys, I'm really struggling with an equation that I have to use for a piece of coursework. I think I'm missing something really basic but I can't seem to get past it and wondered if somebody else could help. I want to know if it's possible to find the Laplace transform of the following...

Hello, I've got some questions for the hardcore analytical mathematicians and electronic engineers. The context: A gain relation in a circuit of RCL and dependent sources ends up in an H(s) which is a quotient of polynomials in s. Number of poles is the number of energy storing...

matlab: >> ilaplace(exp(-1*s)/(s+3)^3) ans = 1/2*heaviside(t-1)*(t-1)^2*exp(-3*t+3) But I think there should be an additional exp(3) multiplied by all. =exp(-1*s)/(s+3)^3 =exp(-1*(s+3)+3)/(s+3)^3 Taking out exp(-3t). In above step I did (s+3)+3 because exp(-3t) says all...

Homework Statement Find the laplace transform of t sin(t) and t cos(t), and the inverse transform of \frac{1}{(1+s^2)^2} 2. The attempt at a solution I found the two laplace forms: \frac{2s}{(s^2+1)^2} and \frac{s^2-1}{(s^2+1)^2} I guess I'm supposed to use the two laplace...

Fick's second law in general form: \frac{\partial C}{\partial t} = D\nabla^2 C In spherical form: \frac{\partial C}{\partial t} = D\frac{1}{r^2}\frac{\partial}{\partial r}\left( r^2\frac{\partial C}{\partial r} \right) (Assume all changes in phi and theta to be zero, so we are only concerned...

Homework Statement What is the inverse Laplace transform of Y(s)/(s+1) ? Homework Equations The Attempt at a Solution I think it is e^(-t) * y(t). Am i right?