Laplace Definition and 1000 Threads

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...

Trying to answer the question: x"+3x'+2x=u(t-1)+2(t-2)u(t-2), x(0)=1, x'(0)=-1 My book has the answer but I need to see how to solve a problem like this. Professor didn't have time to cover this section but he said one of these might be on the test. Any help is greatly appreciated.

< 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...

23.) y'' + 2y' + y = 4e-t; y(0) = 2, y'(0) = -1 Y(s) = [(as + b) y(0) + a y'(0) + F(s)]/(as2 + bs + c) My attempt: a = 1, b = 2, c = 1 F(s) = 4 L{ e-t } = 4/(s+1) (From Laplace Transform Table) Plugging and simplifying: Y(s) = (2s2 + 5s + 7)/[(s + 1)(s2 + 2s + 1) Here is where I get...

Homework Statement f(t) = e^t when 0≤t<1 and 0 when t≥1 Homework Equations Laplace transformations The Attempt at a Solution so the Laplace integral becomesfrom 0 to 1 ∫e^(st^2)dt + 0 how do I integrate this?

Homework Statement How can I take the Inverse Laplace Transform of $F(s) = \frac{d}{ds}\left(\frac{1-e^{5s}}{s}\right)$? I have tried going with inverse of the derivative and convolution (even tried evaluating the derivative and go from there) but although I can get to some results none of them...

Solve by Laplace Transforms. So I'm stuck on how to find this $$\mathcal{L}^{-1}$$ $( \frac{\frac{5s}{4} + \frac{13}{4}}{s^2+5s+8} ) $ I'm not sure what t odo. I was thinking I need to use the $\cos(at)$ and $\sin(at)$ formulas but I'm not sure... Any help would be great

Solev by Laplace Transforms $y'' - 5y' + 6y = 1$ $y(0) = 1$, $y'(0) = 0$So I am getting stuck. Here's my work $s^2Y - 5sY + 6Y = \frac{1}{s} + s - 5$ multiplied through by $s$ to get $s^3Y - 5s^2Y + 6sY = 1 + s^2 - 5s$ so: $Y = \frac{1+s^2-5s}{s^3-5s^2+6s}$ so: $1+s^2-5s = \frac{A}{s} +...

Solve by Laplace Transforms. $y'' + 4y' + 4y = e^t$ $y(0) = 1$, $y'(0) = 0$So I've got $s^2Y - s + 4sY - 1 + 4Y = \frac{1}{s+1}$ then I got: $ Y = \frac{s^2+2s+2}{(s+2)(s+2)}$ Now here is where I am getting lost on the partial fraction decomposition.. I've got $s^2+2s+2 = A(s+2) + B$ I...

I was wondering whether this can be done: Let's say you have transfer function that goes like this: \frac{Y(s)}{U(s)}= \frac{N(s)}{D(s)} Now let's say I divide my transfer into two: \frac{Y(s)}{Z(s)}= N(s) \frac{Z(s)}{U(s)}= \frac{1}{D(s)} Can I apply the Laplace Inverse to these two...

in an example in my text i don't see how they got the "sU" for the transform. actually, i don't even see it in my table of transforms.

Hello PF! We were doing mass balances on mixing tanks in one of my ChemE courses, and in one of the problems we arrived at the following DE: \frac{dC_B}{d \theta} + 0.025C_B=0.0125 e^{-0.025 \theta} Where CB is the concetration of salt in the tank and θ is time. The professor made us solve the...

Hello! I have a question about an equation. I have an equation which is a boundary condition to a problem I have concerning fluid flow in a layered porous medium. I have a equation where my only variable is the temperature T, and I have 10 boundary conditions with it. In order to solve the...

And also: y`+2y=2(1-e^-2t) Y(0)=0 y¨-2y`+y = t+e^t y(0)=1 and y`(0)=0 Please help me out here folks ;)

Hi. I`m new here and I need some help with Inverse Laplace Transform: f(t)=5+3t+e^3t g(t)=(t+1)u(t-2) g(t)=(t^2-9t+20)u(t-5) and Laplace Transform: F(s)=1/(s+2)^5 F(s)= 2s^2+10/s(s^2+2s+10) G(S)=2s/s^2+4e^-sso if anywone can please help me:)

Hi, Please I need some help, how can I get the Laplace transform of the integration of a difference equation?? $\int _{ 0 }^{ \infty }{ { e }^{ -st } } \int _{ -\tau }^{ 0 }{ G(\theta )x(t+\theta )d\theta } dt$ Many thanks in advanced.

I'm trying to solve Laplace equation using Fourier COSINE Transform (I have to use that), but I don't know if I'm doing everything OK (if I'm doing everything OK, the exercise is wrong and I don't think so). NOTE: U(..) is the Fourier Transform of u(..) This are the equations (Laplace...

I need to know what's the Residue Theorem for a Laplace Transform. Does anyone know the name or something, so I can search it? I couldn't find anything. For example, if I have this two equations: X(s).(s-1) = -Y(s)+5 Y(s).(s-4) = 2.X(s)+7 I know how to solve them using Simple Fractions, but...

Hi everyone! :) Have a problem here I can't solve atm. Solve the Laplace transform, when: My try: Would really appreciate some help!

Hello everyone, I have a question about integrating in Laplace Transform. For example, if I have: f(t)=e^{i.t} I have to solve this equation: \int_{0}^{\infty}e^{i.t}.e^{-s.t}dt If I do like this, it's very simple...

Homework Statement use laplace transforms to solve the differential equation y"+2y'+17y = 1 Homework Equations Initial conditions are y(0) = 0 y'(0) = 0 The Attempt at a Solution so it converts to Y(s) (s^2+2s+17) = 1/s which then ends up as; Y(s) = 1/s*1/(s^2+2s+17) i know i need to invert...

What is the non-differential form of the Biot-Savart law? Is it: B=mi*I/(4R*pi)*(cos(a)-cos(b)) or B=mi*I/(4R*pi)*(cos(a)+cos(b))? For a infinitely long conductor, the law is: B=mi*I/(2R*pi) because a=0 and b=pi. So I would say that the correct expression is the one where the cos are...

Homework Statement solve the following differential equation using Laplace transforms: y'' + 4y' + 4y = t^2 e^{-2t}, y_0 = 0, y'_0 = 0 y_0 and y'_0 are initial conditions. Homework Equations Using L to represent the Laplace transform, we have that L(y) = Y L(y') = pY - y_0 L(y'') =...

Homework Statement Give the inverse Laplace transform of F(s) = (-3/s) + (e^-4s)/(s^2) + (3e^-4s)/s Homework Equations Inverse Laplace [e^(-cs) F(s)] = f(x-c)u(x-c) The Attempt at a Solution I'll break this into 3 parts. Part 1 - (-3/s) -3/s = -3(1/s) -> inverse laplace of -3(1/s) = -3...

Homework Statement take inverse laplace of: 6/[s^4(s-2)^2] Homework Equations 6/[s^4(s-2)^2] The Attempt at a Solution I used partial fractions. I was wondering if It could be manipulated to where I could use the laplace table?

Homework Statement Find H(s) = \frac{Y(s)}{X(s)} \frac {d^2y(t)}{dt^2} + a\frac {dy(t)}{dt} = x(t) + by(t) Homework EquationsThe Attempt at a Solution [s^2 + as - b] Y(s) = X(s) H(s) = \frac{1}{s^2+as-b} I assume the inverse is a sign or a cosine but unsure which one.

Homework Statement find the inverse laplace Homework Equations L^(-1)[(s+1)^2/(s+2)^4] The Attempt at a Solution included in attachment. the top problem, #20.

Homework Statement Find F(S) Homework Equations L[e^(2-t)U(t-2)] The Attempt at a Solution a = 2 and using the laplace table I got: e^(-2s)/(s-2) answer should be: e^(-2s)/(s+1)

Homework Statement I do not know how to find f(t) with the given Ampliture 40 and a=pi Homework EquationsThe Attempt at a Solution I have the solution above. my set up was 1/2y''+y'+5=f(t) 1/2S^2* Y(s) + Y(s)+5=f(t)

Homework Statement I'm given a transfer function C(s)=10R(s)/(s+4) And I have to find c(t) for r(t)=6u(t) The Attempt at a Solution First I did this problem by taking inverse laplace of the transfer function, and inserting the value of r(t) in it. Next I did the same problem by first...

Homework Statement This is example 3.9 in Griffiths Electrodynamics. "A specified charge density σ(θ) (inclination angle) is glued over the surface of a spherical shell of radius R. Find the resulting potential inside and outside the sphere." The problem suggests that although it is possible to...

Homework Statement Solve the integral y(t) + \int_0^t (t-u)y(u) \, du = 3sin(2t) Homework EquationsThe Attempt at a Solution Rewrite the equation: y(t) = 3sin(2t) - \int_0^t (t-u)y(u) \, du I assume the integral to be the convolution: f(t) * y(t) = t * y(t) as f(t-u) = f(t) = t...

Homework Statement Solve the IVP : dy/dt + y = f(t) y(0) = -5 where f(t) = -1, 0 <= t < 7 -5, t >= 7 y(t) for 0 <= t < 7 = ? y(t) for t >= 7 = ? Homework EquationsThe Attempt at a Solution So I have never seen a problem of this type, excuse my silly mistakes if I'm interpreting this question...

Homework Statement Determine the Laplace transform of the given function: f(t) = sin(t) for 0 <= t < \pi and f(t) = 0 for \pi <= t Homework EquationsThe Attempt at a Solution Ok, I've been having some trouble figuring out how I should write the above branched function (sorry for the...

Inverse Laplace transform \mathcal{L}^{-1}[F(p)]=\frac{1}{2\pi i}\int^{c+i\infty}_{c-i\infty}F(s)e^{st}dp=f(t) Question if we integrate along a straight line in complex plane where axis are Re(p), Im(p), why we integrate from c-i \ínfty to c+\infty? So my question is, because Im(p) are also...

Homework Statement Find L[x(t)], where $$ x(t) = tu(t) + 3e^{-1}u(-t) $$ Also determine the region of convergenceHomework EquationsLaplace properties, Laplace table: L[te-at = 1/(s+a)2 L[u(t)] = 1/s L[t] = 1/s2 The Attempt at a Solution I don't really know what to do with this as my table...

Homework Statement Division by s Equals integration by t: For this problem use the following property (see relevant equations) to find the inverse transform of the given function: F(s) = \frac{1}{s(s-1)} Homework Equations L^{-1}(\frac{F(s)}{s}) = \int_{0}^{t} f(\tau)\,d \tau The Attempt...

Homework Statement If L[x(t)] = (s + 4)/(s2 + 1), find L[tx(t)] Homework Equations Laplace transform: F(s) = 0∫ f(t)e-stdtLaplace table The Attempt at a Solution Clearly it's not just asking for a Laplace transform. Not sure what it's specifically asking to be honest. t multiplied by...

Homework Statement x(t) = cos(3πt) h(t) = e-2tu(t) Find y(t) = x(t) * h(t) (ie convolution) Homework Equations Y(s) = X(s)H(s) and then take inverse laplace tranform of Y(s) The Attempt at a Solution L(x(t)) = \frac{s}{s^2+9π^2} L(h(t)) = \frac{1}{s+2} I then try to find the partial...

Homework Statement A 4-pound weight stretches a spring 2 feet. The weight is released from rest 15 inches above the equilibrium position, and the resulting motion takes place in a medium offering a damping force numerically equal to 7/8 times the instantaneous velocity. Use the Laplace...

Homework Statement x(t) = cos(3πt) h(t) = e-2tu(t) Find y(t) = x(t) * h(t) (ie convolution) Homework Equations Y(s) = X(s)H(s) and then take inverse laplace tranform of Y(s) The Attempt at a Solution L(x(t)) = [πδ(ω - 3π) + πδ(ω + 3π)] L(h(t)) = \frac{1}{s+2} Laplace Transform inverse ...

Hi, i am new to Laplace transforms/Algebra. I have been given a worked example by lecture to calculate the Laplace transform for a ramped input into a single pole RC high pass filter. i have managed to calculate the Laplace for the Ramp and the Laplace for the Filter. however i can't figure out...

Homework Statement I keep getting the wrong answer, and wolphram seems to back me up. Here's the system of equations ##(-10+s)X(s)-7Y(s)=\frac{10}{s}## ##X(s)+(-2+s)Y(s)=0## Homework EquationsThe Attempt at a Solution Using Cramer's rule I've got...

Find the LT and specify ROC of: x(t) = e-at, 0 ≤ t ≤ T = 0, elsewhere where a > 0 Attempt: X(s) = - 1/(s+a)*e-(s+a) integrated from 0 to T => -1/(s+a)[e-(s+a) + 1] Converges to X(s) = 1/(s+a) , a ⊂ R, if Re{s} > -a for 0≤t≤T Elsewhere ROC is empty (LT doesn't exist). Is this...

Mod note: Please don't tinker with SIZE tags. Things are perfectly readable without them. Homework Statement Find x(t) = L-1[(4e-4s - 3)/(s2 + 6s + 25)]. Homework Equations L(x(t)) = ∞∫∞x(t)e-stdt L-1(x(s)) = (1/2π)(σ - ∞j)∫(σ + ∞j)[x(s)est]ds, "But you want to avoid this integral." Laplace...

So I'm currently taking electricity and magnetism and I'm expected to know how to perform a separation of variables on laplace equation in 2 dimensions.I have taken Zero differntial equations courses and I literally have no freaking idea what's going on. The book I use doesn't spend any time...

Homework Statement I have a circuit with resistor and inductor (RL) that is placed serial and a power supply. the voltage is constant 50 V at t=0 , R=10 ohm, and L=0.2 H. Find the I using laplace transformation Homework Equations - The Attempt at a Solution my attempt is transform everything...

<< Moderator Note -- thread moved to the Homework Help forums >>[/color] I'm stuck on a problem, and I'm in serious need of help. I) Problem: Find the solution to f (t) = 2 \int^t_0 f'(u) sin 3 (t-u) \ du + 2 cos (3t) . Also find f (0) .II) Solution, so far: F(s) = 2 (s F(s) - f(0)) *...

Hello everyone, I have spend whole day but still not figure out an inverse Laplace transform. Hope someone can help me. The question is in the attachment. I'm trying to extract u^2/4D^2 out the bracket to match the standard inverse table, but it seems difficult to deal with the square root...

Homework Statement we have to solve the given circuit using laplace transform for i(t) for t>0 when switch k opened at t=0.. now all I wnated to make clear is the final circuit diagram of this in s-domain..[/B]Homework EquationsThe Attempt at a Solution as I solved I considered the circuit to...