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4
questions
0
votes
2
answers
63
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Approximation of Small Perturbation [closed]
From Morin's Classical Mechanics, on the chapter of Small Oscillations in Lagrangian Mechanics, he does this approximation on the last equality, I don't understand what happened there.
I get the first ...
- 109
5
votes
2
answers
922
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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
11
votes
3
answers
2k
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Why do we ignore the second-order terms in the following expansion?
Consider the expansion done for the kinetic energy of a system executing small oscillations as done in Goldstein:
A similar series expansion can be obtained for the kinetic energy. Since the ...
1
vote
3
answers
2k
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Second derivative of energy as frequency of oscillations [closed]
Is there a way to algebraically see why when I take the second derivative of a potential energy in a point where it is minimal (force is zero), I generally get the frequency (squared) of the ...
- 1,028