Questions tagged [laplace-transform]
Use for the Laplace integral transformation.
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questions
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19 views
Green's Function for Laplace Equation [closed]
I've learned about the definition of green's function, but i'm having trouble when the equation is Laplace equation. Previously, I've learned about the Poisson equation in 2-dimension : $\nabla^2 u=f(\...
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0answers
13 views
Steady State Solution atom light interaction
I am trying to solve a problem about a differential equation which describes the population of states in a atom-light interaction system.
The differential equations are given by:
$$i\hbar\dot{c}_g(t)=\...
-1
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1answer
337 views
What are the real world applications involving Laplace transforms? [closed]
Laplace transform is really interesting. Speaking about Fourier transform, there are many real world applications like we use in removal of noise and Laplace transform is again the extension of ...
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97 views
Mechanical impedance and dynamic stiffness of a mass, spring, damper system including Coulomb friction
I'm trying to understand the concepts of mechanical impedance and dynamic stiffness, what do they mean and if/how they differ. Consider the very simple system below:
Image curtesy of Joshua ...
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26 views
Laplace transform for damped waves
In Zeidler's book on QFT, page 94 there is a definition for a Laplace transform that reads
\begin{equation}
(\mathcal{L} f)(\mathcal{E}) = \int_0^\infty e^{i\mathcal{E}t/\hbar}f(t) dt,
\end{equation}
...
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2answers
49 views
Is time constant the same for linear system for all time?
I have heard that if you take a measurement $T_1$ and wait, then take another measurement $T_2$ and then find $\Delta T = T_2 - T_1$. Then 63% of $\Delta T$ + $T_1$ will represent the measurement when ...
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21 views
Second order linear filter and coefficients sign
Courses on automatics define usually the second order transfer function as
$$
H(s) = \frac{1}{s^2/w_n^2 + 2z/w_n s + 1}
$$
(see here or here for instance )
However, it assumes that the coefficents $...
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1answer
118 views
RLC - CLR - RCL Transfer function
I have problem because I don’t understand the difference between CLR RLC and LCR, they are the same no ? They have the same composant just placed in different ways, I did already found the Transfer ...
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1answer
182 views
Diffusion equation with time-dependent boundary condition
I was trying to solve this 1D diffusion problem
\begin{equation}
\dfrac{\partial^2 T}{\partial \xi^2} = \dfrac{1}{\kappa_S}\dfrac{\partial T}{\partial t}\, , \label{eq_diff_xi}
\end{equation}
with ...
1
vote
1answer
537 views
Density of states for 3D simple harmonic oscillator
I have the thermal partition function and the density of states for the 3D simple harmonic oscillator, which are given below
$$
Z(\beta) = \frac { 1 } { \left( 2 \sinh \left( \frac { \beta \omega } { ...
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vote
1answer
319 views
Laplace transform on thermodynamics equation
I'm trying to create a simple model of a single-flash geothermal plant which consist of 3 main parts (flash-separator, turbine, and condenser). Is there any way to create a transfer function using ...
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1answer
223 views
Why is the Laplace Transform essentially never used when dealing with problems involving resonance?
Both the Laplace Transform and the Fourier Transform can be applied to a PDE, for example the wave equation, and used to derive a solution to the equation.
But I never see the Laplace Transform used ...
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506 views
Laplace Transform Density of States & Partition function
I am currently going through Pathria's Statistical Mechanics text , and under the Canonical Ensemble description, the author stresses that the partition function of a continuous system is the Laplace ...
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0answers
195 views
Fourier Transforms of Harmonic Functions
Suppose you are presented with the equation ($D=3$)
\begin{equation}
\nabla^2 A(x) = \nabla^2 B(x).
\end{equation}
Decompose $A$ and $B$ into their Fourier components,
\begin{equation}
A(x) = \int d^...
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3answers
294 views
Why is there a sudden change in current between $t=0^{-}$ and $t=0^{+}$ when an active inductor is connected in series with a relaxed inductor?
Let us take the following question as an example:
For the above question I drew the corresponding Laplace transform diagram, as follows (didn't draw the switch since it basically open circuit after $...
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vote
1answer
104 views
Difference between Fourier and Laplace transforms in analyzing data
I have a set of displacement-time graphs from an experiment to convert to the frequency domain. Both the Fourier and Laplace transform seem to do this, so what's the difference between them (...
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1answer
264 views
What is this equation, written on a wall? [closed]
I've also asked this in MathOverflow, but since the equation in question is related to acceleration and physical phenomenon, I figure this is also a good place.
I was asked to ID the following, but ...
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73 views
Question about the Radiative Transfer Equation (RTE) Phase function term
I am new to this subject. I am trying to understand what is the purpose of the phase function
$$
∂u/∂t=-v∘∇u-v( μ_{a}+μ_{s})u+∫vμ_s p_{s} (Ω^{'}→Ω)u(r,Ω^{'},t)ⅆΩ^{'}+q(r,Ω,t)
$$
Were
u= angular ...
10
votes
2answers
1k views
Why is the impedance of a resistor the same in time and frequency domains if the Laplace transform of a constant is not the same constant?
I'm sure this is a silly question, but if the Laplace transform of a constant is not a constant, e.g.
$$\mathfrak{L}[1] = \frac{1}{s}$$
then how come the impedance of a resistor is the same in the ...
1
vote
1answer
6k views
Solving LR Circuit with Laplace Transform
I have a RLC circuit where the capacitor is connected in parallel with a resistance and inductance in series. The battery is connected "in parallel" with the capacitor and the RL branches. At t=0 the ...
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2answers
804 views
Express Laplace transform of voltage across a capacitor in terms of charge
In Charge Tunneling Rates in Ultrasmall Junctions section 2.1, the authors consider the problem of charge relaxation in a simple circuit shown in Figure A.
The implicitly use an assumption made about ...
