1. Boltzman Oscillation

    Engineering Help finding the damping ratio formula for this circuit

    The circuit to be analyzed is shown below: Since initial conditions are zero (from the instructions) I will use laplace transforms for the cirucit and I will use the MAME method to solve this circuit. The laplace transforms that are required will give me: $$E_g(s) = \frac{10}{s}$$ $$ L_3...
  2. SamRoss

    I Why is the Laplace transform unchanged when t is replaced with -t?

    In Mathematical Methods in the Physical Sciences by Mary Boas, the author defines the Laplace transform as... $${L(f)=}\int_0^\infty{f(t)}e^{-pt}{dt=F(p)}$$ The author then states that "...since we integrate from 0 to ##\infty##, ##{L(f)}## is the same no matter how ##{f(t)}## is defined for...
  3. J

    A Can I linearize this equation?

    By using the laplace transform: $f(t)=sin(Φ(t))$ I want it in the form: F(S)/Φ(S) The purpose is to linearize it in order to put it into a larger transfer function, so far my only solution is to simplify it using taylor expansion.
  4. A

    I Accuracy of the Normal Approximation to Binomial

    What is the preferred method of measuring how accurate the normal approximation to the binomial distribution is? I know that the rule of thumb is that the expected number of successes and failures should both be >5 for the approximation to be adequate. But what is a useful definition of...
  5. D

    Problem finding the output voltage using Laplace transform

    1. Homework Statement The input signal of the circuit shown below is ##x(t)=2\sin (ω_ot + \pi/6)##. The switch in the circuit is controlled with a digital signal of the form ##s(t)=\sum_{k=-\infty}^{+\infty} (u(t+ε-kT_s) - u(t-ε-kT_s))##, ##\frac{2\pi}{T_s}=800\pi##, ##ε\to 0##, so that when...
  6. mjtsquared

    I Region of convergence of a Laplace transform

    If a Laplace transform has a region of convergence starting at Re(s)=0, does the Laplace transform evaluated at the imaginary axis exist? I.e. say that the Laplace transform of 1 is 1/s. Does this Laplace transform exist at say s=i?
  7. marsupial

    Engineering The effect of a switch in a Laplace circuit analysis

    1. Homework Statement The switch in the circuit in has been closed for a long time. At the switch is opened. a) Find i0 for t>=0 (b) find v0 for t>=0 I don't understand the effect of the switch in the position it is in. It's acting as a short circuit, I think, so presumably the capacitor...
  8. T

    Characteristic equation in terms of the Laplace operator

    1. Homework Statement The stability of a spinning body may be explored by using equation (3.40), with no torque components present. It will be assumed here that the spin is about the z -axis and has a rate ωZ = S. 2. Homework Equations $$I_{xx}\dot{ω} - (I_{yy}-I_{zz})Sω_y = 0$$...
  9. JTC

    A Causality in differential equations

    Hello, I am studying control theory. And I have encountered something I have never considered or thought about. Consider a system with y as the output differential equation and u as the input. any(n) + ... + a1y(1) + a0y = bmu(m) + ... + b1u(1) + b0u Here, the subscripts indicate...
  10. JTC

    Best way to learn control theory for mechanical engineers

    Hello, I have begun to teach myself Control Theory. I am looking for a book that is focused for mechanical engineers. I do not mind examples in electrical engineering, but they bore me (no offense). Also, I find some books begin with Laplace Transforms. Yet I found this online lecture...
  11. C

    Finite element solving of Laplace's equation doesn't converge

    1. Homework Statement I'm trying to solve Laplace's equation numerically in 3d for a charged sphere in a big box. I'm using Comsol, which solves using the finite elements method. I used neumann BC on the surface of the sphere, and flux=0 BC on the box in which I have the sphere. The result does...
  12. Cocoleia

    Laplace & Inverse Laplace transforms

    1. Homework Statement I am given this equation: and asked to solve using Laplace transforms 3. The Attempt at a Solution This is what I did: This seemed logical to me, I used partial fractions and it stayed pretty simple. This is what the solutions my prof posted do: Is my answer...
  13. G

    Engineering Analysis of a servo motor

    1. Homework Statement 2. Homework Equations I'm studying a mathematical behaviour of a servo motor and I need some help to understand it. The output signal is \$\beta (t)\$, representing the angle rotated by the axis at instant t, in relation to the equilibrium position. On the servomotor...
  14. A

    Solving partial differential equation with Laplace

    1. Homework Statement am trying to solve this PDE (as in the attached picture) also my attempt is included, but i stopped in step, can you help me with it? appreciated, 2. Homework Equations 3. The Attempt at a Solution my attempt is the same as in the...
  15. JTC

    I Meaning of the word "Harmonic" in different contexts

    A harmonic function is one that satisfies Laplace's equation -- a definition cannot be more precise than that. However, in the study of vibrations, sine and cosine are considered harmonic functions; but they don't solve Laplace's equation. And then there are words like: harmonics (for higher...
  16. Cocoleia

    Using Laplace to solve circuit analysis

    1. Homework Statement 3. The Attempt at a Solution As you can see, the answer is given in the problem. I have the 0.8t par right but somewhere along the way I messed up. I'm not really to sure about how to solve these types of problems using Laplace. Is there a general procedure that I...
  17. D

    Inverting Shifted Laplace function

    1. Homework Statement A beam is supported at one end, as shown in the diagram (PROBLEM 11 page 281 of Lea, 159 of the course pack). A block of mass M and length l is placed on the beam, as shown. Write down the known conditions at x = 0. Use the Laplace transform to solve for the beam...
  18. J

    A Can you solve (a-bx)y'+(c-dx)y-e=0 with a,b,c,d,e constants?

    I'm having trouble solving the differential equation (a-bx)y'+(c-dx)y-e=0 with a,b,c,d,e constants. I tried laplace transforming it, but then I end up with yet another differential equation in the laplace domain because of the xy and xy' terms.
  19. mattyboson12

    Control systems -- input with non-zero initial conditions

    1. Homework Statement Deriving an s-domain equation for the following inputs a) &b) 3. The Attempt at a Solution I understand how to derive the equation for an input with zero initial conditions (part a) but I'm not sure what to do when there are non-zero initial conditions (part b)
  20. G

    I Does Laplace's demon know about entropy?

    Hi. I read this thread with great interest and have similar question: In a deterministic universe, does entropy exist for Laplace's demon? Since he knows the universe to it's microstate, does the term "macrostate" even make sense to him? And say there is a "half-demon" that only knows the...
  21. Z

    Inverse Laplace help

    1. Homework Statement F(s) = \frac{s^2e^{-4s}}{s^2+9} 2. Homework Equations \mathcal{L} ({f(t-a)\mathcal{H}(t-a)}) = e^{-as}F(s) 3. The Attempt at a Solution F(s) = e^{-4s}(\frac{s^2}{s^2+9}) using \mathcal{L} {f(t-a)\mathcal{H}(t-a)} = e^{-as}F(s) f(t) =...
  22. kostoglotov

    Which inverse Laplace form can I use?

    1. Homework Statement I have the second order diff eq: Solving by Laplace transform gets me to: I could use the inverse laplace transform that takes me back to e^{at}cos(bt) with b=0, but that only solves for the homogeneous (complementary) part of the equation, it won't reproduce the...
  23. Pouyan

    Laplace Transform of this function

    1. Homework Statement We want to find the Laplace transform for f(t): 0 for t≤2 and (t-2)2 for t≥2 2. Homework Equations I know that Lap{uc f(t-c)} = e-csLap{f(t)}=e-csF(s) I rewrite f(t)=0+g(t) where g(t) = 0 for 0≤t<2 and (t-2)2 for t≥2 so we can write f(t)=g(t)=...
  24. C

    Establishing equations for a worm screw mechanism

    Hey guys :) So I'm looking to form equations that I can apply a Laplace transformation to. The mechanism specifically is a trailer jack - it converts rotational motion to linear motion. And its high torque provides a mechanical advantage to lifting heaving loads. Can anyone help me form...
  25. S

    Engineering Eigenfunctions of the vector Helmholtz equation

    Hi everyone, I'm looking for a reference book that treats the theory behind the eigenfunctions solution of the so called vector Helmholtz equation and its Neumann and Dirichlet problems. I've already found a theory inside the last chapter of Morse & Feshbach's Methods of theoretical physics...
  26. J

    Low Pass Filters and Laplace Transform

    1. 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. 2. Homework Equations 3. The...
  27. astrodeva

    Solving Laplace Equations using this boundary conditions?

    The equation is Uxx + Uyy = 0 And domain of solution is 0 < x < a, 0 < y < b Boundary conditions: Ux(0,y) = Ux(a,y) = 0 U(x,0) = 1 U(x,b) = 2 What I've done is that I did separation of variables: U(x,y)=X(x)Y(y) Plugging into the equation gives: X''Y + XY'' = 0 Rearranging: X''/X = -Y''/Y = k...
  28. chrispypatt

    Final Value Theorem Rule Clarification

    My homework problem is as follows: Consider the Laplace transform shown below. (4s3+15s2+s+30)/(s2+5s+6) a. What is the value of f(t=0) and f(t=∞)? Use the initial and final value theorems. b. Find the inverse transform f(t). Use this expression to find f(t=0) and f(t=∞) and compare with the...
  29. ELiT.Maxwell

    Point charge inside a electrically neutral cavity in conduct

    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...
  30. D

    Laplace tranform of unitstep (heaviside) function

    1. Homework Statement 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)] 2. Homework...