# Questions tagged [laplace-transform]

Use for the Laplace integral transformation.

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### Calculating Fourier Coefficients for this 50% bipolar square wave [closed]

I'm getting stuck trying to derive an equation for the Fourier coefficients of this waveform. Following along from this example: https://lpsa.swarthmore.edu/Fourier/Series/ExFS.html It is clear that ...
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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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### Fourier and Laplace transforms (Forster's Hydrodynamics book)

In Forster's hydrodynamics textbook, he defines the following Fourier transform and (one-sided) Laplace transform \begin{align} S(k,\omega) =& \int_{-\infty}^{\infty} dt e^{i\omega t} S(r,t) \\ \...
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### Inverse Laplace transform for Debye function

Given $$D_n(x)=\frac{n}{x^n}\int _{0}^{x}\frac{t^n}{e^t-1}dt,$$ the Debye function. Wikipedia says that it computes the Heat capacity of the Debye model. Mathematically, we are interested in the ...
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### 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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### Laplace transform for damped waves

In Zeidler's book on QFT, page 94 there is a definition for a Laplace transform that reads $$(\mathcal{L} f)(\mathcal{E}) = \int_0^\infty e^{i\mathcal{E}t/\hbar}f(t) dt,$$ ...
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### 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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### 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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### Diffusion equation with time-dependent boundary condition

I was trying to solve this 1D diffusion problem $$\dfrac{\partial^2 T}{\partial \xi^2} = \dfrac{1}{\kappa_S}\dfrac{\partial T}{\partial t}\, , \label{eq_diff_xi}$$ with ...
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### 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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### 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 ...
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I'm trying to get a transfer function of $F=ma$ in the Laplace domain. This should be simple, but yet I'm confused. The transfer function is displacement over force. So, I have two approaches. First ...