3 votes
Accepted

Should natural frequency be modeled using molecules?

Normally, when we talk about molecules in a solid vibrating, we mean that the vibrating molecule is moving back and forth with respect to the lattice/its surrounding molecules. The amplitude of this ...
David_h's user avatar
  • 72
2 votes
Accepted

How can the Rabi frequency be complex?

Maybe the confusion comes from the fact that we use the name "Rabi frequency" for two slightly different things: the typical frequency of Rabi oscillations (which is a real number) and the ...
Matteo's user avatar
  • 2,879
2 votes
Accepted

What is the spectrum of a broken square drum?

Actually, you’ll still need to impose boundary conditions on the fourth side. A free side would rather correspond to a Neuman boundary condition. Say your square is $[0,1]^2$ (setting $L=1$), and $u$ ...
LPZ's user avatar
  • 10.9k
2 votes

How to standardize the energy of a Dirac delta function relative to sample rate (width) and amplitude?

For a sampled signal, a one sample pulse has a white DTFT (discrete time Fourier transform) spectrum. A wider pulse has a high frequency cutoff. The energy in the pulse is proportional to its duration,...
John Doty's user avatar
  • 20k
1 vote

Is it possible to, like white noise, excite all audio frequencies equally, but with a more immediate & less random burst? Like a signal discontinuity?

A step has a $f^{-2}$ power spectrum, not white. A delta function (impulse) has a white noise spectrum. You may approximate it with a narrow pulse. A pseudorandom binary sequence or pseudonoise ...
John Doty's user avatar
  • 20k
1 vote
Accepted

Orbital frequency of gravitational wave prior to merger

To make the algebra easier let's absorb all the constants into a single constant and write: $$ \frac{d\omega}{dt} = k\omega^{11/3} $$ Then integrating gives: $$ \tfrac{-8}{3}\omega^{-8/3} = kt + C $$ ...
John Rennie's user avatar
1 vote

Damped Quantum Harmonic Oscillator with sinusoidal driving force

It is usually convenient to write problems about a quantum harmonic oscillator in terms of the creation-annihilation operators $a^\dagger$, $a$. The Schrödinger equation now looks like $$ i\hbar\frac{\...
Gec's user avatar
  • 5,222
1 vote

Measuring the tension of a drumhead

As Chemomechanics has pointed out and as discussed in some detail here, the equations are related to the solution of the wave equation on a circular membrane. The solution corresponding to the ...
Puk's user avatar
  • 13.4k

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