Laplace transform Definition and 752 Threads

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...

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?

Homework Statement Find the laplace transform of; t*u(t-1) I always thought that the laplace transform of the function was; (1/s^2) * (e^-s) However, recently I was told that I was wrong! I was told that I was wrong, because t*u(t-1) is not a function of (t-1). That in order...

Homework Statement Solve by Laplace transforms the following y'' + y = t when 0</=t<1, and = 1 if t>/=1 Homework Equations L{y''} + L{y} = L{f(t)} The Attempt at a Solution By Laplace transforms I get L{f(t)} = (1 - e^-s) / s^2 and Y(s) = (1-e^-2 + s^2) / s^2 (s^2 +1) But I cannot...

What is y = L{Y(s)} for Y(s) = (1 - e^-s + s^2) / (s^4 + s^2)? Note: F(s) = L{f(t)} = (1 - e^-s) / s^2 I've just been going in circles trying to figure this one out. I tried simplifying it by partial fractions, but I still couldn't figure it out, and I'd appreciate some help.

Homework Statement \frac{\partial^{2}u}{\partial t^{2}} = a^{2} \frac{\partial^{2}u}{\partial x^{2}} (x>0, t>0) with u(0,t) = t, u(x,0) = 0, ut(x,0) = A. Solve the PDE using laplace transform. The Attempt at a Solution I have managed to get the transform: \frac{\partial^{2}U(x,s)}{\partial...

Homework Statement Bessel's equation of order zero can be written xy''+y'+xy=0 Homework Equations Denote the solution which is finite a the origin by J[SIZE="1"]0 Show that the Laplace transform of J[SIZE="1"]0 is proportional to (s^2+1)^-1/2 The Attempt at a Solution

Homework Statement Problem: laplace transform of x"+2x'+x=sin(t) x=x'=0 Homework Equations The Attempt at a Solution Attempt at problem: I was able to get Y(s)=1/(s^2+1)(s^2+2s+5) and then i expanded it to get [s/10(s^2+2s+5)]-[s/10(s^2+1)]+[1/5(s^2+1)]. The last two terms are...

Hi, I know that in order to inverse a function f(s) back to its time domain counterpart, f(t), one must use the line integral, the Bromwich Integral, but I do not know how to evaluate a line integral. Does anyone know of any practical methods of evaluating the inverse Laplace transform, could...

Homework Statement find the laplace transform of g(t) = t u(t-2) using the basic definition. Homework Equations L{f(t)} = ∫f(t)e-stdt from 0 to infinity The Attempt at a Solution I am able to get the transform by applying the t-shifting property. However, how do I do it by using...

Homework Statement If I had something like, et*u1(t), how would I convert it to F(s) Homework Equations ua(t)*f(t-a) = e-asF(s) The Attempt at a Solution From the general equation of transformation, I don't have f(t-a) and I don't think I can make one out of the exponential...

G(S)=2/s(e^-3s_e^-4s) G(S)=(2S+1/S^2)*e^-2s_(3s+1/s^2)*e-3s find g(t)?

Hi I understand most of the steps in the determination of the time scale. But i don't really understand the step in equation 6.96. The first attachment is the full details of the time scale, and the second attachment is the part which I am stuck on. I just want to know, how they get...

Homework Statement Is it possible to do the inverse laplace transform for this? F(s) = \Sigma[e^(ns)]/s where n=0 and goes to infinity Homework Equations u_c(t) = [e^-(cs)]/s The Attempt at a Solution I don't think I can use this conversion because c or s is never less than...

Hi, I am trying to solve the damped harmonic oscillator: \frac{d^2y}{dt^2}+\frac{b}{m} \frac{dy}{dt}+\frac{k}{m}y=0 and I thought using the Laplace transform might do the trick. Anyway so I did the LT (and inserted the initial conditions that at t=0 y=A, and dy/dt=0) and obtained...

(d^n/dt^n)f(t)= ?? im not entirely sure how to solve this problem...

Homework Statement Determine the inverse Laplace transform of 1/((s^2 +1)*(s-1)). The answer is 1/2*(e^x - cos(x) - sin(x)). Homework Equations We get a table of known inverse Laplace transforms. The Attempt at a Solution I tried to break this up using partial fractions...

Problem; If, f(t) = d/dt [(e^-5t) (cos2t)] Find F(s). Eh, well, I don't really know what to do, can I get some pointers? Am I supposed to integrate both sides, so I can get rid of d/dt, and then apply the integration property to find the answer?

Homework Statement Solve the IVP for t>0 y'(t)+\int^{t}_{0}y(\tau)d\tau = =sin(t) for 0<t<=pi =0 for t>pi y(0)=-1 The Attempt at a Solution The solution depends on how large t is and therefore the solution consist of two parts depending on the size of t.. Let's call them y1(t)...

Hi, I'm doing some preparation work for an upcoming mathematics module at University and I'm going over some Laplace transform questions. Part of one question asks for the Laplace transform of sin(ωt – Φ) and after looking the transform up I've found the answer to be (ω)cos(Φ) + (s)sin(Φ)...

I know the final result, its on all the charts. But I need to show step by step how to get the solution. If someone could help out by getting me in the right direction or just plain giving me the answer, that would be much appreciated:smile:.

hello. I have transformed the Laplace transform into the infinite series by repeatedly using integration by parts. What is this infinite series? may be Laplace transform series, or only an infinite series without name? L(t)= \int_{t}^{\infty}\frac{f(t)}{e^{st}} dt =-0 +...

Ok i have two questions, one i am unsure of and one i don't have a clue how to correctly find it. Homework Statement You have to work out the inverse function of: 4s/ s^2+4s+8 The Attempt at a Solution I think the answer is: 4e^(-2t)*(cos2t+sin2t) Is this correct? Homework...

Homework Statement Find the inverse laplace transform of (s+1)/ (s^2 + 4s + 5) + e^-2s / 3s^4 Homework Equations The Attempt at a Solution For the first one (s+1) / (s^2 + 4s + 5), I completed the square for the denominator so (s+1) / [(s+1)^2 + 1] Now it gets...