Laplace transform Definition and 752 Threads

Homework Statement Using: \mathcal{L}\big\{t^n\big\}=\frac{n!}{s^{n+1}}\text{for all s>0} Give a formula for the Laplace transform of an arbitrary nth degree polynomial p(t)=a_0+a_1t^1+a_2t^2+...+a_nt^n Homework Equations \mathcal{L}=\lim_{b\rightarrow\infty}\int_{0}^{b}p(t)e^{-st}dt The...

Homework Statement Given that r(t) = L^-1 (Inverse laplace) *H(S) and by making the link between the time-domain and frequency-domain responses of a network, explain in detail why the ideal “brick-wall” lowpass filter is not realisable in practice. [/B]Homework EquationsThe Attempt at...

Homework Statement Given the Laplace transform $$F_L(s) = \frac{1}{(s+2)(s^2+4)},$$ by using the complex inversion formula compute the inverse Laplace transform, ##f(t),## for the following regions of convergence: (i) ##Re(s)<-2;## (ii) ##-2<Re(s)<0;## (iii) ##Re(s)>0.## Homework Equations...

hi, sorry for the bad english. exist a Laplace Transform of tanh(x)? i know math of high school, so sorry if it is a question a little silly thanks

Evening All I have had a go at a laplace transform and got stuck. $$\frac{d^2v}{dt^2}+\frac R L \d v t+\frac 1{LC}v=\frac 1{LC}V_0$$ $$R=12 \Omega, L=0.16H, C=10^{-4}F, V_0=6V, v(0)=0, v'(0)=0$$ so subbing these in i get $$\mathscr L \left[ \frac {d^2v}{dt^2}+75\d v t+62500 v...

y(t) = u(t - a) . x(t) u(t) is a unit step function. I have to find Y(s)/X(s). Do I have to do convolution in frequency domain?

Homework Statement A process can be represented by the first order equation (4δy(t)/δt) + y(t) = 3u(t) Assume the initial state is steady (y = 0 at t = –0). (a) Determine the transfer function of this process in the s domain. (b) If the input is a ramp change in u(t) = 4t, determine the...

The closest Inverse Laplace Transform from my table is $\displaystyle \begin{align*} \mathcal{L}^{-1}\,\left\{ \frac{2\,a\,s\,\omega}{\left( s^2 + \omega ^2 - a^2 \right) ^2 + 4\,a^2\,\omega ^2 } \right\} = \sin{ \left( \omega \, t \right) } \sinh{ \left( a \, t \right) } \end{align*}$ so we...

Homework Statement (2s^2) +10s / (s^2 -2s +5 )(s+1) , I have checked the partial fraction , it's correct , but according to the ans it's (e^t)[(3cos2t + 2.5sin2t)] - (e^-t), but my ans is (e^t)[(3cos2t + 4sin2t)] - (e^-t)Homework EquationsThe Attempt at a Solution

Homework Statement [/B] http://www.dartmouth.edu/~sullivan/22files/New%20Laplace%20Transform%20Table.pdf (see item 26a) homogenous solution to underdamped in amplitude phase form: (see attached image) 2. Relevant info - non zero initial conditions: x(t=0) = xo AND dx/dt(t=0) = vo - unforced...

Hello everyone, I was studing Heaviside's operators for solving ODE, which I strongly recommend to have a look because it helps a lot when the differential equations have "exotic" inhomogeneous terms, but it is a method that works and you do not know exactly why. Some biographies tell that...

x(t) and y(t) are related by y(t)=1/(x(t) -k), how should I derive Y(s)/X(s)?

for the right part of the notes, why the integral of (e^-su)f(u) from 0 to T will become integral of (e^-st)f(t) from 0 to T suddenly ? why not integral of (e^-s (t-nT) )f(t-nT) from 0 to T ? as we can see, u = t +nTd given/known dataHomework EquationsThe Attempt at a Solution

Homework Statement g(t) = (t+1)us(t) - (t-1)us(t-1) - 2us(t-1) - (t - 2)us(t-2) + (t-3)us)(t - 3) + us(t-3) Homework Equations unit step function us(t-3) is same as u3 (t) Shift in time: L[f(t - T)us(t-T)] = e-TsF(s) us(t) ↔ 1/s t ⇔ 1/s2 The Attempt at a Solution 1/s2 + 1/s - e-s/s2 + e-s/s -...

Homework Statement Diagram for a vehicle suspension is given. Displacement of wheel is given by 'x' and and displacement of body is 'y'. Spring constant, k = (7*10^4) Nm Damping coefficient, c = (3*10^3) N/m/s mass,m = 250kg a) Make a Laplace Transform of system and utilize it to predict 'y'...

Homework Statement Solve the following initial value problem using Laplace transforms: y' + 4y = 3t3 e−4t ; y(0) = 0 . Useful information: Recall that the Laplace transform of y 0 is pY − y(0), where Y is the Laplace Transform of y. The Laplace transform of tk e−at is k!/(p + a)k+1 . Confirm...

Homework Statement Use Laplace transform to solve the following ODE Homework Equations xy'' + y' + 4xy = 0, y(0) = 3, y'(0) = 0 The Attempt at a Solution L(xy'') = -\frac{dL(y'')}{ds} L(4xy) = -\frac{4dL(y)}{ds} L(y'') = s²L(y) - sy(0) - y'(0) = s²L(y) -3s L(y') = sL(y) - sy(0) - y(0) =...

Hello everybody! I'm sorry if it's not the right section to post in. I'm trying to solve this exercise: $$\frac{1}{2i\pi}*\int_{8-i\infty}^{8+i\infty}\frac{e^{s(t-5)}}{(s+4)^2}ds$$ The request is to find the result in function of $$t$$ I know i must use the Riemann inversion formula, and so the...

Did I do this right?View image: 20151201 152557

Did I do this right? View image: 20151201 143310 1

I'm working on a few problems to find Laplace transforms and I got stuck on this one. ${U}_{3}(t){(t-3)}^{5/2}$ It looks different from the other I've been doing so I don't really know how to get started

Homework Statement xy''+y'+xy=0, y'(0)=0, y(0)=0 Using the method of Laplace transforms, show that the solution is the Bessel function of order zero. Homework Equations -(d/ds)L{f(x)} The Attempt at a Solution The only thing I got out of this when trying to solve it was y=0. Obviously not...

Homework Statement L-1{(2s2+3)/(s2+3s-4)2} The Attempt at a Solution I factored the denominator f(t)=(2s2+3)/((s-1)(s+4))2 now I've tried partial fractions to get (2s2+3)/((s-1)(s+4))2 = A/(s-1)2 + B(s+4)2 (2s2+3)=A(s+4)2 + B(s-1)2 by substitution, s=1 and s=-4 5=A(25) A=1/5 35=B(25)...

Homework Statement L-1{3/s1/2} Homework EquationsThe Attempt at a Solution 3L-1{1/s1/2} 3L-1{(1/sqrt(π))(sqrt(π)/(sqrt(s))} 3/(sqrt(π))L-1{(sqrt(π))/(sqrt(s))} 3/(sqrt(π))(1/(sqrt(t)) This is what I got from the solution for this problem. What tipped them off to multiply by sqrt(π)? And...

Homework Statement The differential equation given: y''-y'-2y=4t2 Homework EquationsThe Attempt at a Solution I used the laplace transform table to construct this equation,and then I did partial fraction for finding the inverse laplace transform.But I'm now stuck at finding the inverse laplace...

How would I take the laplace transform of f(t)= te^tsin^2(t)?

Homework Statement [/B] I know for t[u(t)-u(t-2)], we can simplify that to tu(t)-((t-2)+2)u(t-2) which then gives us tu(t)-(t-2)u(t-2)-u(t-2). Now, the laplace transform seems trivial but I am having problems with this equation: sin(t)[u(t)-u(t-pi)] Homework...

The ordinary differential equation, with initial values,shall be solved using Laplace transform. The ODE looks like this \begin{equation} y''(t')+2y''(t)-2y(t)=0 \end{equation} And the initial conditions are \begin{equation} y(0)=y'(0)=0, y''(0)=0 \end{equation} The problem is with the first...

Kindly help me find the Inverse laplace transform of the attached.

Homework Statement Use laplace transforms to find following initial value problem -- there is no credit for partial fractions. (i assume my teacher is against using it..) y'' + 2y' + 2y = 2 ; y(0)= y'(0) = 0 Homework Equations Lf'' = ((s^2)*F) - s*f(0) - f'(0) Lf' = sF - f(0) Lf = F(s) The...

Homework Statement Use laplace transforms to find following initial value problem -- there is no credit for partial fractions. (i assume my teach is against using it..) y'' - 4y' + 3y = 0 ; y(0)=2 y'(0) = 8 Homework Equations Lf'' = ((s^2)*F) - s*f(0) - f'(0) Lf' = sF -...

Homework Statement y'' + 3y' + 2y = r(t), r(t) = u(t - 1) - u(t - 2), y(0) = y'(0) = 0. I need to solve this by convolution, which I know is commutative. The problem is that my calculation gives (f * g) =/= (g * f). Could someone please tell me where my mistake is? Homework Equations...

Homework Statement So I know 1/(s-a)=e^(a1), but why is say, 2/((s+4)^2) equal to 2xe^-4x? Do I just simply add an X if the numeration is a constant other than 1?

Homework Statement Let ##f(t)= \begin{cases} \sin t , \; \; 0 \le t < \pi \\ 0 , \; \; \; \; \; \text{else.} \end{cases}## Use Laplace transform to solve the initial value problem ##x'(t)+x(t)=f(t), \; \; \; x(0)=0.## Homework Equations Some useful Laplace transforms...

Homework Statement y'' + 4y = 8t^2 if 0 < t < 5, and 0 if t > 5; y(1) = 1 + cos(2), y'(1) = 4 - 2sin(2). Use the Laplace transform to find y. Homework Equations t-shift, s-shift, unit step function. The Attempt at a Solution I have been trying to solve it for hours, but keep getting the wrong...

Homework Statement Here is an imgur link to my assignment: http://imgur.com/N0l2Buk I also uploaded it as a picture and attached it to this post. Homework Equations u_c (t) = \begin{cases} 1 & \text{if } t \geq c \\ 0 & \text{if } t < c \end{cases} The Attempt at a Solution Question 1.1 -...

Homework Statement [/B] Having a little trouble solving this fractional inverse Laplace were the den. is a irreducible repeated factor 2. The attempt at a solution tryed at first with partial fractions but that didnt got me anywhere, i know i could use tables at the 2nd fraction i got as...

Homework Statement Prove that http://www4f.wolframalpha.com/Calculate/MSP/MSP26931c1531g07285beh7000062h7f6g1ggd95eea?MSPStoreType=image/gif&s=5&w=98.&h=38. =http://www4f.wolframalpha.com/Calculate/MSP/MSP6901c153574d0bdbh20000048829f0g4d1fi1d0?MSPStoreType=image/gif&s=5&w=69.&h=35. The...

i have read many of the answers and explanations about the similarities and differences between laplace and Fourier transform. Laplace can be used to analyze unstable systems. Fourier is a subset of laplace. Some signals have Fourier but laplace is not defined , for instance cosine or sine...

Can anybody direct me towards a proof of the second shifting theorem for Laplace transforms? I'm understanding how to use it but I can't figure out where it comes from. I've been learning from Boas, which doesn't offer much in way of proof for this theorem. Are there any good resources online...

hi, if there is a initial value problem with a ζ in it with specified values what do you do with it when taking the laplace transform?

Homework Statement (didn't know how to make piecewise function so I took screenshot) Homework EquationsThe Attempt at a Solution My issue here with this problem is that I have absolutely no idea where to start... I have read through the textbook numerous times, and searched all over the...

Hello guys. I need an easy explanation regarding Laplace Transform and Fourier Transform. I know it is quite a mathematics question but I need an explanation in which it has something to do with engineering. I already search a bit about them but still cannot find and explanation that easy enough...

The unilateral laplace transform integrates from 0 to infinity.Then how can i take laplace transform of exp(t)u(-t)?PS:I don't want to flip it and use time scaling property.

Hi, I have an idea which when tested looks like its clearly flawed. I am hoping someone can tell me where my procedure is flawed, or point me to some other theory that has already done something similar. The first two are the laplace transform. The third line is the Fourier Transform. The...

Homework Statement Homework Equations Laplace Trasformations The Attempt at a Solution a. done b. f(t)= t -3*t*u(t-1) + 4*u(t-1) -3*u(t-2) -2*t*(t-2) c. 1/(s^2) - (3e^-s -2e^-2s)/(s^3) + (4e^-s -3e^-2s)/s d. 1/(s-1) * (1/(s^2) - (3e^-s -2e^-2s)/(s^3) + (4e^-s -3e^-2s)/s) These are the...

Homework Statement f(t)=tcos(4t)Homework Equations tnf(t)=(-1)n dF(s)/dsn The Attempt at a Solution I don't understand why this formula is giving me the oppiste sign of the answer. If I apply the formula I get (16-s2)/(s2+16)2 Because n=1 I need to multiply by a negative but this yields...

Hi all. Sorry about creating this new threat despite existing some others on the same topic. I have a problem in understanding a very specific step in the mentioned proof. Let me take the proof given in this link as our guide. My problem is just at the ending. When it says: "The region...

Homework Statement Solve the following: $$\mathscr{L}_s^{-1} \left\{ \frac{s}{s^2-s+\frac{17}{4}} \right\}$$ Homework Equations Table of Laplace Transforms.The Attempt at a Solution The solution is $$f(t) = (1/4 )e^{t/2} (\sin(2 t)+4 \cos(2 t))$$ I know I need to break up ##F(s)## into...

< Mentor Note -- thread moved to HH from the technical math forums, so no HH Template is shown >[/color] So this is the problem Here is the question: A 32lb weight strecthes a spring 2ft.The weight is released from rest at the equilibrium position. beginning at t=0, a force equal to f(t)= sint...