# Tag Info

## New answers tagged resonance

0

Well, I finally pull it out. I used Green's functions and it was pretty straightforward, For a harmonic oscillator, you have to solve: $(\frac{d^2}{dt^2} + 2b\frac{d}{dt} + \omega^2)G(t-t')= \delta(t-t')$ The solution is for $t>t'$: $$G(t-t')= exp(-b(t-t'))\frac{\sin(\omega'(t-t'))}{\omega'}$$ where $\omega' = \sqrt{\omega^2-b^2}$ The solution ...

1

The magnitude of the transfer function (amount of vibration vs amount of excitation) of a harmonic oscillator with damping is shown below (from this Wikipedia article). The Dirac Delta function is white in the frequency domain; meaning that it has equal excitation at all frequencies. So, the motion of the harmonic oscillator is simply the white noise times ...

2

Let's consider a 1D cavity with one wall at $x=0$ and the other wall at $x=L$. We know we have the wave equation for the electric potential $\phi$, $\nabla^2 \phi - \frac{1}{c^2}\partial^2_t \phi = 0$. There would be a similar one for $\vec{A}$ in three dimensions. We additionally have the boundary condition that the potential must be zero on the boundary. ...

-1

The wave touching normal to a reflector must either be an E-mode standing node or anti-node, depending upon whether the interface is a conductor or an insulator. If you want it not to destructively add on reflection, how many half-wavelengths can fit into the gap - and the minimum number?

2

Like Jarosław Komar commented, you are using the wrong value for $n$. It is also easy to visualize this by looking at what the longest standing wave would look like in an air column with only one open end: Where the wavelength, $\lambda$, is defined as: $$\lambda=\frac{v}{f}$$ So the fundamental frequency would require a $n=0$, since the length of the air ...

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