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-1
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1answer
21 views

Forced damped harmonic motion, angular frequency at which amplitude is maximum. differentiation [closed]

How would I differentiate this with respect to the driven angular frequency (equating to zero) in order to obtain the max value of the amplitude in terms of these components?
1
vote
1answer
36 views

Oscillation of Atom

What exactly does it mean when one says 'one atom of Caesium 137 oscillates 9,192,631,770 times'? I do understand the general thing about oscillation but what exactly is the oscillation of atom, what ...
-5
votes
0answers
23 views

effect of earth's magnetic field on period of pendulum [duplicate]

I want to know will earth's magnetic field change period of pendulum if pendulum is made up of- 1. ferromagnetic material 2. paramagnetic material.
0
votes
0answers
24 views

How long does it take for disturbed water to stop making sound?

Suppose I have a bowl with water or another liquid. The water from the bowl is perfectly quiet. Then I throw a stone in the water and I wait. How can I calculate the time after which the water is ...
4
votes
1answer
143 views

Why is the wave equation so pervasive?

The homogenous wave equation can be expressed in covariant form as $$ \Box^2 \varphi = 0 $$ where $\Box^2$ is the D'Alembert operator and $\varphi$ is some physical field. The acoustic wave ...
3
votes
3answers
98 views

What is the time period of an oscillator with varying spring constant?

It is well known that the time period of a harmonic oscillator when mass $m$ and spring constant $k$ are constant is $T=2\pi\sqrt{m/k}$. However, I would be interested to know what the time period ...
1
vote
1answer
29 views

What really is the significance of the resonant frequency in terms of “ease of vibration”?

I was studying the concept of resonant frequency and I've read quite a few articles and notes on it. What I have understood from what I have read is that the resonance frequency of an object is its ...
1
vote
2answers
239 views

Oscillation of a Bose Einstein condensate in a harmonical trap

We were asked to try to make a theoretical description of the following phenomenon: Imagine a 2D Bose Einstein condensate in equilibrium in an harmonical trap with frequency $\omega$. Suddenly the ...
0
votes
0answers
36 views

Period for small oscillations is like simple harmonic motion

In Arnold's book on mechanics there is the following problem: Consider the period of oscillations near a minimum $E_0$ of the potential energy function $U$. Then he says to compute the limit of ...
0
votes
0answers
35 views

Separation of time scales to solve ODEs

I am reading several papers that obtain approximate solutions to nonlinear ODEs using a "standard technique" to separate the time scales of the dynamics. For examples, consider the ODE (a particle in ...
2
votes
2answers
203 views

Showing that a mass moves a half cycle

Consider a mass $m$ at position $x(t)$ on a rough horizontal table attached to the origin by a spring with constant $k$ (restoring force $-kx$) and with a dry friction force $f$ $$\begin{cases} ...
0
votes
2answers
78 views

Why is a sine wave considered the fundamental building block of any signal? Why not some other function? [closed]

It is mathematically possible to express a given signal as a sum of functions other than sines and cosines. With that in mind, why does signal processing always revolve around breaking down the signal ...
2
votes
2answers
23 views

What determines the point of energy spillover to higher modes of a standing wave resonator?

One of the better known physics demonstrations for standing wave resonance is the singing rod . By holding the rod exactly in the middle the demonstrator constrains the first mode of excitation - the ...
0
votes
0answers
36 views

Kater's pendulum graph

I was told that the graph of position vs period must be a straight line in Kater's pendulum, but my findings are more curved, also after searching in google graphs are like parabolas, my question is ...
12
votes
2answers
609 views

Small oscillations of heavy string

I'm solving problem in classical field theory and I have some difficulties. I'm trying to study small oscilations of heavy string with fixed points. First of all I wrote down this Lagrangian: ...
8
votes
2answers
321 views

Are there any fully analytically solvable nonlinear oscillators?

I'm trying to find a simple one-dimensional problem, in which a particle would oscillate with some energy, and the period of oscillation would depend on particle energy (unlike in harmonic ...
0
votes
0answers
10 views

Atoms - deflection from the equilibrium state - oscillation [duplicate]

A homogeneous, spherical electron cloud describes an atom (radius $a_0$ and total charge $^−e $ and positive point charge$^+e$ as the nucleus. An external electric field stimulates the electron ...
2
votes
1answer
70 views

Analytical mechanics with SR

Is there an analytical mechanics with SR? Of course you can write down the Lagrangian and Hamiltonian of a free particle. What about non-free? Are there any problems? To be specific: what would the ...
0
votes
2answers
35 views

Equation for vibrating cantilever in SHM

what is the equation connecting the period of oscillation of a ruler/cantilever with its length? my relation indicates that $T\propto L^2$ but i dont know if it is good
5
votes
2answers
194 views

Approximations in simple pendulum

In the approximation $$-(g/ \ell) \sin \theta \approx -(g/ \ell) \theta $$ we make an error $R$ which is $O(\theta ^3)$. If i did well my calculations it is estimated by $$R\leq|(g / ...
8
votes
2answers
3k views

What creates the chaotic motion on a double pendulum?

As we know, The double pendulum has a chaotic motion. But, why is this? I mean, the mass of the two pendulums are the same and they have the same length. But, what makes its motion random? I'm just ...
0
votes
0answers
25 views

Why are springs shaped as they are? [duplicate]

It must have something to do with Hooke's Law and their tendency to have a restorative force as equal to the distorting force as possible; but I'm not sure. Help please?
1
vote
1answer
32 views

Undamped Resonance of a Classical Harmonic Oscillator

Consider an undamped harmonic oscillator. It may be driven at it's natural frequency, $\omega_0^2 = \frac{k}{m}$. According to Feynman, and other sources, were this to happen, the amplitude of the ...
1
vote
2answers
65 views

What is the qualitative cause for a driven oscillator to have a max. amplitude during resonance?

The steady-state motion of a driven oscillator is given by;$$x =\underset{\text{amplitude}} {\dfrac{F_0}{m({\omega_0}^2 - {\omega}^2)}} \cos\omega t.$$ As we see, the amplitude becomes maximum when ...
1
vote
1answer
56 views

General solution of a mass spring system

This is the differential equation that describes small amplitude vertical oscillations of a mass $m$ that is hanging from a spring $$\frac{d^2x}{d t^{2}} + \frac{b}{m}\frac{dx}{dt} + \frac{k}{m} x = ...
0
votes
3answers
77 views

Why is $x=C\cos(\omega t)$ the solution of $m\frac{d^2 x}{dt^2}+kx=F_o\cos(\omega t)$ though lacking two arbitrary constants?

I was studying undamped oscillator with harmonic driving force at the steady-state condition. It can be expressed in the form of differential equation as:$$m\dfrac{d^2 x}{dt^2}+kx=F_o\cos(\omega t).$$ ...
1
vote
0answers
40 views

What is the mechanism of subharmonic oscillations?

It's clear to me from linear systems theory that energy manifested within a fundamental mode of resonance can saturate with the excess energy spilling over into harmonic frequencies greater than the ...
1
vote
2answers
50 views

Resonance peak broadening due to losses: physical reason

I wonder why when losses are present in a oscillator, the width of the resonance peak is broadened. More precisely: why, when losses are present, can the amplitude reach nearly the maximal one (the ...
0
votes
2answers
55 views

In general terms, what key elements are necessary for resonance to exist in a physical system?

I found a related question An Analogy for Resonance, and John Rennie gives a good explanation using description of the harmonic oscillator. But I'm really looking for an accurate and complete list of ...
3
votes
1answer
34 views

Polarisation by Reflection - oscillation direction

I'm currently studying polarisation by reflection, and have come across two pieces of information from the same source, which I can't seem to understand on how they differ. The oscillation direction ...
0
votes
1answer
45 views

Definition of mechanical impedance

Mechanical impedance is in the simplest (yet common) case defined as: $$ Z_m = \frac{F}{v} $$ where $F$ is force (let's assume 1D case) and $v$ velocity of the object (let's assume point of mass). ...
1
vote
1answer
47 views

How to calculate the period of the movement from a potential?

I have an assignment, where I have an object moving in 1-D with a given mass and energy, and the potential V(x), and I'm supposed to calculate the period of the movement as a function of the energy ...
2
votes
1answer
64 views

Calculating pendulum rate variation due to change in force of gravity over arc of swing

Hi all and thank you in advance for any insight into this problem. I'm a journalist working on a story on precision pendulum clocks and specifically on the isochronism of pendulums. I note that the ...
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votes
3answers
11k views

Does the human body have a resonant frequency? If so, how strong is it?

Inspired by this question on Music beta SE, I'm wondering if the human body has a strong resonant frequency. I guess the fact that it's largely a bag of jelly would add a lot of damping to the system, ...
0
votes
1answer
46 views

Energy dissipation in damped oscillator (not driven by any external force)

If I have a damped oscillator (with no driving force), the energy of the oscillator will decrease like: $$E(t)=E_0e^{-\gamma t},$$ where $E_0$ is some initial energy and $\gamma\in\mathbb R^ +$. We ...
1
vote
1answer
49 views

Analysis of motion of a body moving on a string?

I was wondering about something I observed yesterday. To give some background, one of my hobbies is slacklining. This is essentially like tight-rope walking but with a one inch piece of (in this case ...
2
votes
1answer
428 views

Coupled Oscillators

This is an exercise of my last exam. Since I couldn't find anybody who solved it or knows how to, it would be really nice if somebody could tell me if my thoughts on it go into the right direction. ...
0
votes
0answers
30 views

Ratio of oscillation amplitudes of a box on a gasket to floor

So the problem is that I have a box and I put it on a gasket to preserve it from vertical oscillations. The gasket is compressed by the box by a quantity of $h$. The floor is oscillating at frequency ...
1
vote
1answer
62 views

Quantum Harmonic Oscillators

I'm having trouble with quantum harmonic oscillators and I'm not sure how to approach these questions: . I'd really like to get my head around these concepts but I'm struggling to understand fully. ...
0
votes
0answers
19 views

How does the phase of an alternating current change when flowing through a multi-layered material?

I have questions regarding the properties of the alternating electrical current in the following imaginary experiment: There is an AC (sinusoidal wave with frequency $f = 5\ \mathrm{Hz}$). I would ...
0
votes
0answers
13 views

Does a pendulum oscillate in liquid [duplicate]

What will the rate of oscillation be in the liquid? I know that it won't be equal to that of air. I have done a couple of internet searches and couldn't get a satisfactory answer.
1
vote
2answers
122 views

Period of a simple pendulum accounting for friction

The period of a simple pendulum is $$T=2\pi\sqrt{\ell/g},$$ but no where in there do I see that it accounts for friction. Does it somehow account for friction, and if not, how could you do that?
9
votes
3answers
1k views

Will a violin string keep vibrating for a longer time in vacuum than in air?

Hitting a string of a violin or a guitar will cause that string to vibrate, but after short time the amplitude of the vibration will decay, consequently the produced sound will die out. I suppose ...
5
votes
2answers
108 views

What is a full cycle in damped oscillation?

Maybe it seems a dumb question, but I can't understand what the cycle in a damped oscillation is? Let's take an example: In harmonic motion, one cycle is the smallest distinguishable part of wave ...
6
votes
2answers
544 views

Is the usually taught solution to forced harmonic motion just a special solution?

Let's say we have a mass on a spring being driven by a forcing function. Given hook's law, $F = -kx$, and a forcing function of $$F(t) = F_0\sin(\omega t) .$$ We can write: $$ m\frac{d^2x}{dt^2} = ...
0
votes
0answers
62 views

discrepancy in theoretical and natural frequency?

In an experiment to determine the natural frequency of a spring-mass-pulley system, why would the experimental natural frequency (found using 1/time) be greater than the theoretical natural frequency ...
0
votes
1answer
26 views

Can the logarithmic decrement be found from extension of spring?

Consider a spring-mass system in which a mass hangs freely from a spring fixed to a ceiling. Can the logarithmic decrement be found simply from the extension of the spring? The only parameters known ...
0
votes
1answer
612 views

Damped oscilator - logarithmic decrement of damping [closed]

Could you please tell me, where is the mistake? What is the logarithmic decrement of damping $Λ$ of damped harmonic oscillator, if its mechanical energy decreases to the 50% of its initial value ...
0
votes
2answers
53 views

Is an oscillation the same as a period?

Is one oscillation from peak to trough to peak again or is it just peak to trough? Doing a homework question and want to be sure I have the right definition
0
votes
1answer
45 views

Building a Crystal Radio Questions

I have been reading several books and articles about building a crystal radio and the explanations about the inner workings of the circuit seem vague. All articles and books mention the coil and the ...