Laplace Definition and 1000 Threads

bear with me, i know that this question has been asked many time , but i would like a definite answer, now, starting off the external charge density on the outer surface of sphere WILL be uniform by unique solution of Laplace equation and letting the sphere be huge, so, electric field due to...

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...

(2.) Let the differential equation ¨x + 2 ˙x + 2x = 6 sin(t)U(t − 3π/2) , x(0) = 2, x˙(0) = 2 Solve for the position function x(t) using the Laplace transform:

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...

Suppose that $u$ is the solution of the Laplace equation $u_{xx}+u_{yy}=0$ in $\{(x,y)\in \mathbb{R}^2: x^2+y^2<1\}$ $u(x,y)=x$ for all $(x,y)\in \mathbb{R}^2$ such that $x^2+y^2=1.$ Find the value of $u$ in $(0,0).$ Use the property of median value.

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...

Let $\Omega$ an open domain in $\mathbb{R}^2.$ Suppose that $u$ is an application $C^2$ that satisfy the Laplace equation $\Delta u=0$ in $\Omega.$ Let $\Omega_{(a,b)}=\{(x+a,y+b): (x,y)\in \Omega\}$ and define $v(X,Y)=u(X-a,Y-b)$ for all $(X,Y)\in \Omega_{(a,b)}.$ Show that $v$ is an...

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...

Homework Statement Use the convolution property to obtain the inverse Laplace transform of F(s)= e-3s * ((3s+15)/s2+25) Homework EquationsThe Attempt at a Solution = (3*(s/s2+52) + 15*(1/s2+52)) *e-3s Using table of Laplace: 3*(s/s2+52) = 3*cos(5*t) = T7 15*(1/s2+52) = 15/5*sin(5*t) =T18 e-3s...

For example: If F(s) = L{t3e-16tcos(3t)sin2(t)} What would L-1{F(s)} be?

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...

Hello everybody! I know how to solve Laplace equation on a square or a rectangle. Is there any easy way to find an analytical solution of Laplace equation on a trapezoid (see picture). Thank you.

Homework Statement Hello, I have just started studying Laplace transformations and I am struggling to identify reverse Laplace transforms. I understand how to perform the transform, but going the other way is really confusing me. i.e, given ##F(P)## find ##f(t)##. If I have that ##F(P) =...

Homework Statement Solve the Laplace equation inside a sphere, with the boundary condition: \begin{equation} u(3,\theta,\phi) = \sin(\theta) \cos(\theta)^2 \sin(\phi) \end{equation} Homework Equations \begin{equation} \sum^{\infty}_{l=0} \sum^{m}_{m=0} (A_lr^l + B_lr^{-l -1})P_l^m(\cos...

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 I'm suppose to verify the given Laplace in (a) Cartesian (b) Sperical and (c) Cylindrical coordinates. (a) was easy enough but I need to know if I'm doing (b) and (c) correctly. I don't need a solution, I simply need to know if the my Spherical formula is correct, my...

Homework Statement Find the Inverse laplace transform of: http://www4c.wolframalpha.com/Calculate/MSP/MSP14541hg721e74730d4fb00004644i96f59549h1d?MSPStoreType=image/gif&s=30&w=201.&h=40. Result...

Homework Statement I uploaded the question as a picture and attached it. Homework Equations Unit step function - u_c (t) = \begin{cases} 1 & \text{if } t \geq c \\ 0 & \text{if } t < c \end{cases} Impulse function - δ(t) = \displaystyle\lim_{Δ\rightarrow 0} δ_Δ (t) Multiplication Property...

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 I uploaded the problem statements as a picture as well. I have completed these and was wondering if someone could check my work, and let me know if it is correct. Problem 1.3: Find the expression for the transfer function of this linear time-invariant causal system with...

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...

I am trying to numerically calculate the electric potential inside a truncated cone using the finite element method (FEM). The cone is embedded in cylindrical coordinates (r,phi,z). I am assuming phi-independence on the potential, therefore the problem is essentially 2D; I am working only with...

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...

Homework Statement ##y'' + 2y' + 2y = h(t); y(0)=0, y'(0)=1, h(t) = \begin{cases} t &, \pi \leq t < 2\pi \\ 0 &, 3\pi \leq t < \infty \\ \end{cases}## 2. Homework Equations The Attempt at a Solution Take the Laplace of both sides:[/B] ##\mathcal{L}(y'' + 2y' + 2y) = \mathcal{L}(h(t))...

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...

Hi, I'm dealing with an exam problem (which i have 8 days to solve, with no outside help limitations), which is to write a fortran95 program that solves linear systems. the first part asks to find the determinant of a NxN matrix with the laplace expansion, implementing it as a recursive...

hi , i was asked to solved this but i have no idea how to laplace y^4, can anyone please help? its the question in the middle

Hello, When evaluating the step response of a circuit, the resulting Laplace representation is: $\frac{I_{pd}}{s^2 C1 R1}$ If I look this up on a table of Laplace Transforms, this results in $\frac{I_{pd}*t}{C1 R1}$. However, I'm struggling to solve this via partial fraction expansion--is...

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...

I have completed the exercise, but I did something weird in one step to make it work, and I'd like to know more about what I did...or if what I did was at all valid. 1. Homework Statement Show that Laplace's equation \frac{\partial^2u}{\partial x^2}+\frac{\partial^2u}{\partial...

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 Homework Equations Laplace Transforms The Attempt at a Solution Using basic physics knowledge I got m1a1=-k1x1+k2(x2-x1) and m2a2=-k3x2-k2(x2-x1) Sub in values and use laplace transforms and rearrange partial fraction and I found that By doing this I am assuming...