All Questions
Tagged with harmonic-oscillator classical-mechanics
225
questions
5
votes
5
answers
808
views
How can I interpret the normal modes of this mechanical system?
How can I interpret the normal modes of this mechanical system?
The equations of motion for the system are as follows:
$$\left[\begin{array}{ccc}
m_{1}\\
& m_{2}\\
& & 0
\end{array}\...
- 51
0
votes
1
answer
97
views
Action-angle variables for three-dimensional harmonic oscillator using cylindrical coordinates
I am solving problem 19 of ch 10 of Goldstein mechanics. The problem is:
A three-dimensional harmonic oscillator has the force constant k1 in the x- and y- directions and k3 in the z-direction. Using ...
- 13
1
vote
0
answers
41
views
Oscillating body and Doppler effect
Say we have a body attached to a spring, oscillating with some frequency $\nu$. This is one of the simplest problems studied in elementary Physics, and yet I've noticed we always study it positioning ...
- 1,616
0
votes
0
answers
33
views
What are the different types of resonances in forced oscillation systems?
I'm currently studying resonances in systems subjected to forced oscillations and have come across various terms and cases that I'd like to understand more clearly. Specifically, I am analyzing a ...
0
votes
1
answer
42
views
Velocity Formula in SHM
In Simple Harmonic Motion in one dimension, if we assume
$$\text{Displacement}=x=A \text{sin} (\omega t+\phi)\implies \text{velocity}=v=A \omega \text{cos} (\omega t+\phi)$$
From here by substitution ...
- 347
0
votes
1
answer
17
views
Interpretation of perpendendicularity of paths
Two particles are oscillating along two close parallel straight lines
side by side, with the same frequency and amplitudes. They pass each
other, moving in opposite directions when their ...
- 347
1
vote
0
answers
56
views
Probabilistic reformulation of classical Simple Harmonic Oscillator
As an interesting exercise, I was wondering whether we could reformulate classical mechanics in such a way that we could use the same mathematical paradigm we use in quantum mechanics. I'll expose it ...
- 1,616
1
vote
4
answers
113
views
Directly integrating the Lagrangian for a simple harmonic oscillator
I've just started studying Lagrangian mechanics and am wrestling with the concept of "action". In the case of a simple harmonic oscillator where $x(t)$ is the position of the mass, I ...
- 13
0
votes
2
answers
57
views
Does the motion of a simple pendulum shifts to SHM, due to damping?
I have doubt in damping oscillations of a pendulum. Let's consider a simple pendulum in a drag medium like air. Suppose if the angular displacement (theta) is larger (say 40°), the oscillations start ...
- 43
0
votes
0
answers
90
views
Classification of equilibrium configurations for particles subject to elastic force constrained on a circle
I am interested in classifying all the possible equilibrium configurations for an arrangement of $l$ equal point particles $P_1, P_2, . . . , P_l$ $(l > 2)$ on a circle of radius $R$ and centre $O$....
- 130
0
votes
2
answers
47
views
Quantum position in molecular vibration
Evere molecule consists of atoms that vibrate around their equilibrium positions. This can be viewed from a classical or a quantum perspective. However, I found a seeming inconsistency between these ...
- 1,440
2
votes
2
answers
137
views
Classical limit of quantum harmonic oscillator
I have read that if in the quantum harmonic oscillator, $n$ is very large, then the probability density is similar to the classical one.
In the case of a simple harmonic oscillator:
$$P_{clas}=\frac{1}...
0
votes
2
answers
186
views
Equations of motion for coupled harmonic oscillators
We just started QFT, and I'm following our professor's notes but there is a passage I do not understand. We are speaking about a system of $N$ coupled harmonic oscillators $y_j(t)$ for $j = 1, ..., N$ ...
- 361
0
votes
2
answers
343
views
Solving forced harmonic oscillator differential equation using fourier transform
I am trying to solve the equation of a forced harmonic oscillator using Fourier Transform. I know that if a function $f(t)$ is such that $\lim_{x->\pm \infty} f(t) = 0$, then
$$\frac{1}{\sqrt{2\pi}}...
1
vote
3
answers
210
views
Harmonic oscillator with constant external force
I tried to find the full derivation of the differential equations for the following problem but did not find any relevant resources that discuss external forces with harmonic motion (except damped and ...
- 150