# Questions tagged [anharmonic-oscillators]

Problems concerning oscillators that are not harmonic (i.e. for forces that are not linearly proportional to position).

101 questions
Filter by
Sorted by
Tagged with
42 views

• 21
113 views

### Anharmonic effects in crystals, help with intuition

I've been reading a bit about how it is necessary to consider anharmonic effects in crystals if one wants to properly understand things like thermal expansion etc. So for example here: So the cubic ...
• 23
1 vote
97 views

• 436
109 views

### Nonlinear PDE from Chain of Oscillators

Some years ago, I was reviewing the calculation for the dynamics of limiting case for a chain of springs with transverse oscillations and found a partial differential equation for which I haven't been ...
• 121
922 views

### Rigorously prove the period of small oscillations by directly integrating

This answer proved that $$\lim_{E\to E_0}2\int_{x_1}^{x_2}\frac{\mathrm dx}{\sqrt{2\left(E-U\!\left(x\right)\right)}}=\frac{2\pi}{\sqrt{U''\!\left(x_0\right)}},$$ where $E_0:=U\!\left(x_0\right)$ is a ...
• 123
334 views

### Why is the bending mode of carbon dioxide harmonic?

Here's a simple classical model of a carbon dioxide molecule: This gif illustrates the "bending mode" vibration. If the carbon atom moves a small distance $\mathrm{d}x,$ then the springs' ...
• 53.2k
66 views

• 197
1 vote
133 views

• 427
282 views

### Time period of an anharmonic but periodic motion [closed]

How do I find the time period of anharmonic motion given an expression of force as a function of $x$? This is the question I was solving: $$U(x)=k|x|^3$$ where $k$ is a positive constant. If the ...
• 1,233