Questions tagged [laplace-transform]
Use for the Laplace integral transformation.
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Laplace Transform of time evolution of Amplitudes involving correlation functions
The correlation function is given by
$$
G_{ij}(t-t')= g_{i} g_{j} e^{(i\omega_{i0}-\frac{\Gamma_{0}}{2})t-(i\omega_{j0}-\frac{\Gamma_{0}}{2})t'}
$$
With the time evolution of amplitudes being given by
...
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What is the difference between scaling property when scaling factor is $-1$ and the time reversal property of Laplace transform?
I came across this question when one of my students asked me about it.
Suppose that $L$ denotes the Laplace transform and that $L\{F(t)\}=f(s)$. By scaling property, we have $L\{F(-t)\}=-f(-s)$. The ...
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Laplace transform: How to evaluate partial derivative in the denominator of a fraction?
I am solving a differential equation using the Laplace transform. However, to evaluate it I need to evaluate some strange terms. Specifically, I have a partial derivative in the denominator of the ...
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First passage time for state transitions expressed in Laplace space?
I'm struggling to understand the reasoning between moving between two steps in a biophysical reaction scheme for a paper I am reading. For this (from the description), the probabilities over different ...
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Unique distribution of charge on a conductor
If i place some charge on a conductor then it will distribute itself in such a way that electric field everywhere inside is zero. My text book says that only one kind of such charge distribution is ...
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PI controller - output calculation [closed]
The propeller of an airship is connected to a DC motor. The motor is being controlled using a PI controller. The PI controller has a proportional gain of Kp = 2, and an integral gain of Ki = 0.5, and ...
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Fourier vs. Laplace transforms
Electronics books often use Laplace to analyze circuits, while in physics we use Fourier, most of the times... if not always: from complex impedances to electromagnetism, quantum mechanics, Green ...
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What is the physical meaning of sigma in the Laplace transform?
Let’s use a simple harmonic oscillator as an example. When we calculate the Fourier Transform (a special case of the Laplace transform) of that system we get a function that shows which frequencies of ...
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What is the intuitive interpretation of the transfer function of this system?
If I have the system that could be observed in the next Image:
I want to know the transfer function, where the external force $f$ is the entry and $x_1$ is the output. The direction and positive ...
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Harmonic oscillator boundary condition issue for an impulse force
I am trying to solve an equation of an underdamped harmonic oscillator with a damping, and I get a weird boundary condition that perplexes me. Let me precise the issue, the equation is :
\begin{...
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Finding the Frequency and Damping Ratio of a Mass Spring Damper excluding Air Resistance
In summary, I need the damping ratio and damped frequency of a system excluding air resistance, as the system will be operating in a vacuum. The system can be modeled as a mass-spring-damper, and the ...
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Using laplacian transform to derive a general solution to the quantum harmonic oscillator
I'm unhappy with the often used approach of guessing the form of the solution and working from there. In the case of the quantum harmonic oscillator, once the form
\begin{equation}\frac{d^2 \psi(x)}{...
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Transfer function of system of coupled 2nd order ODE
I am wondering how to calculate transfer function $H(s)$ of system described by 3 coupled differential equations. The pourpose of work is to calculate "Bodedx" diagram ($|H(i\omega)|(\omega)$...
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Temperature distribution using Laplace transform
Consider room that occupies quarter space That is formed by two walls.
One wall is fully insulated and has a constant temperature $0$.
Another wall has a window of length L that with one edge at the ...
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Laplace transformation with mass
I am doing some QFT calculations with the fermion mass term, and it is making the calculation much more challenging.
Say I have
$$F(t,m) = \int_0^1 dx \frac{1}{1-x}\frac{1}{(t ~(1-x)+m(1-x)^2)^\...
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