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0answers
25 views

How to count such a huge number of oscillation in atomic clock? [duplicate]

A second is defined as time taken for 9,192,631,770 oscillations of caesium hyperfine levels. But it's not exactly that the electron moves up and down between these two levels. So it must be related ...
0
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2answers
40 views

Where is the periodic nature in the Cs atomic clock? [on hold]

In case of pendulum clock,lets say one swing ticks one second..but what is the analogy in case of CAESIUM atomic clock? Is 9,192,631,770 ticks is equivalent to one tick in pendulum clock? And how we ...
0
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1answer
35 views

When a particle oscillates with simple harmonic motion, the period of the oscillation is [on hold]

When a particle oscillates with simple harmonic motion, the period of the oscillation is... a) ...directly proportional to the displacement from the origin b) ...directly proportional to the ...
13
votes
2answers
174 views

Rope waves with a twist

In the picture you see a person walking a slackline. A slackline is a tensioned flatband of polyester. Typical tensions are between 1 kN to 15 kN depending on the length of the line. The lines are ...
1
vote
1answer
89 views

Period of a pendulum [on hold]

In the book 'Calculus the Early Transcendetals' at page 776 (7th edition) they give that the period of a pendulum with length $\text{L}$ that makes a maximum angle $\theta_0$ with the vertical is: ...
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0answers
29 views

Calculating mechanical motion/velocity of a pendulum/swing? [on hold]

I am a bit new to this so sorry if I mess anything up. Just needed some help with this question. A mom puts her 20kg son into a swing seat and pulls him back so he is 3.00m vertically to the lowest ...
12
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3answers
4k 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 ...
1
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3answers
33 views

Vertical oscillator with a punctual mass

Ok, this is apparently a simple problem. Consider a mass bound to a vertical oscillator of constant k, at thr equilibrium position, and initial height H. When letting it move by its own weight, one ...
3
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2answers
75 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
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2answers
39 views

Damped Simple Harmonic Motion Proof? [closed]

I was reading about damped simple harmonic motion but then I saw this equation: $$-bv - kx = ma$$ $b$ is the damping constant. Then it said by substituting $dx/dt$ for $v$ and $d^2x/dt^2$ for $a$ we ...
0
votes
1answer
297 views

Fundamental frequency of a material and its Young's modulus

I wonder if there is a connection between fundamental frequency and Young's modulus of a material. For example, how to calculate the Young's modulus of a glass bar by knowing its frequency spectrum?
0
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0answers
14 views

Difference between Stuart Landau equation and Ginzburg Landau equation

I have to study the Ginzburg Landau equation, but I have been told to begin by a simplier equation: the Stuart Landau one. I understand that both of these equations are used to describe nonlinear ...
1
vote
1answer
45 views

Pendulum motion equation issue

The differential equation that gives the equation of motion of a pendulum where: $m$ is the mass $L$ is the distance between the pivot and the body's centre of mass $g$ is the acceleration due to ...
0
votes
2answers
63 views

Damped Pendulum (generalised)

I know the differential equation for the swinging of a simple pendulum: $\displaystyle\frac{\partial^2\theta}{\partial t^2} + \left(\frac{g}{L}\right)\sin\theta = 0$ where: $L$ is the length of ...
0
votes
1answer
43 views

Lyapunov exponents of a damped, driven harmonic oscillator

I am supposed to calculate Lyapunov exponent of a damped, driven harmonic oscillator given by $\ddot{x} + 2\beta \dot{x} + \omega_0^2 x = f\cos(\omega t)$ Lyapunov exponent is $\lambda$ in $\delta ...
0
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2answers
223 views

Can friction change the resonance frequency of a system?

I am simulating the transient response of a mass-spring-damping system with friction. The excitation is given in the form of a base acceleration. What I am not sure about is: can the friction change ...
0
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0answers
6 views

How to derive Q-factor from damped beam resonator?

Starting with free load ($q=0$) homogeneous beam with damping coefficient $\xi$ $$ EI\frac{\partial^4 w(x,t)}{\partial x^4} +\xi \frac{\partial w(x,t)}{\partial t} +\mu\frac{\partial^2 ...
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0answers
9 views

Explain quality factor and bandwidth [duplicate]

Can anyone explain concept of quality factor and bandwidth with a mechanical example?
0
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1answer
38 views

What is the exact mathematical definition of oscillation/vibration?

My question is basically is what criteria need to be fulfilled to decide wether a motion is osciliiation/vibration or not. I found two definitions, def1: "moving around an equilibrum", def2: ...
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2answers
307 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
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0answers
24 views

Pendulum with Viscous and Frictional Damping

I am trying to model a pendulum with both viscous and frictional (Coulomb) damping. The problem is that the viscous damping only occurs in one direction because I am modeling a dashpot that only has ...
0
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1answer
40 views

Derivation of the wave equation from Hooke's law- Generalization question

Following the derivation on the relevant Wikipedia page, I am having a bit of trouble moving from the following line, with the case of 3 particles in a row: $$ \frac{\partial^{2}}{\partial t^{2}} ...
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3answers
18k 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
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0answers
28 views

Interpretation of contourplot pendulum

I've made this plot of a function that evaluates the size of the angle on the x-axis, and the velocity of the angle for the pendulum on the y-axis. I'm having a hard time interpreting the meaning of ...
0
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4answers
57 views

Is the speed of sound in air constant?

In Optics lecture we took a formula for the speed of a wave which is: $$ v=\frac{\omega}{k} $$ where $\omega$ is number of complete vibrations per second: $$ \omega=\frac{2\pi}{\tau} $$ and: $$ ...
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5answers
159 views

A conceptual doubt regarding Forced Oscillations and Resonance

While studying about the Resonance and Forced Oscillations, I came across a graph in my textbook that is given below:- Now, the author writes As the amount of damping increases, the peak shifts ...
1
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1answer
48 views

Amplitude of damped driven harmonic oscillator [closed]

I have a question that I can reason physically but mathematically I am not sure if my approach is correct. The amplitude of the oscillator is: $$A(\omega) = \frac{QF_{0}}{m}(\frac{1}{\omega_{0} ...
1
vote
1answer
30 views

At what times is the energy in an LC oscillator completely electric or completely magnetic?

I know that the time period of the LC oscillations is given by $T=2\pi\sqrt{LC}$. At what times is the total energy of the circuit completely stored in the capacitor or completely in the inductor?
0
votes
1answer
40 views

Period of oscillation of magnet levitated over another magnet

The situation is similar to what we used to do as kids, take a vertical wood dowel, with a ring magnet placed at the bottom, and another ring magnet opposing it, floating on top. More precisely, it ...
3
votes
1answer
765 views

Why maximum energy transfer at natural frequency even if max amplitude occurs below $f_0$

This is a paragraph from my book: "For a damped system, the resonant frequency at which the amplitude is a maximum is lower than the natural frequency.However, maximum transfer of energy, or energy ...
5
votes
0answers
70 views

Why are vibrations so common? [closed]

Why are vibrations so common? We all know, or pretend to know, that symmetries and the least action principle lead to conservation laws.Is there something more fundamental behind the fact that ...
5
votes
4answers
217 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 ...
0
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0answers
10 views

Colpitts oscillator

why colpitts oscillator is used for fixed radio frequency?I think they are used because it produces frequencies in the radio spectrum am I correct
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2answers
66 views

Pendulum on a train

I've seen multiple questions about a pendulum on a train and most say to use $T = 2 \pi (L/F)^{1/2}$ and I have done this to compare the pendulum's periods before being on a train and then once its on ...
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0answers
8 views

Averaging over periodic functions in the derivation of the Kuramoto model

In the book "Chemical Oscillations, Waves, and Turbulence" Kuramoto derive his phase model. In this derivation he averaged over a fast period T (on page 66): $$ \Gamma(\psi_a - \psi_{a'}) = ...
0
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2answers
56 views

Why can some oscillations be modeled by Simple Harmonic Motion, while others cannot?

For some oscillators an increase in the driving amplitude changes the period (frequency) of the oscillation, but the simple harmonic oscillator does not predict this type of behavior. Why?
3
votes
1answer
38 views

Swing: why does the body position modify the amplitude?

When a person swings, why does the amplitude of oscillations increase if the person changes the body position ? That is, when descending and approaching the vertical position, if the person extend his ...
1
vote
3answers
61 views

Normal mode analysis

I'm reading lots of texts about normal modes and I've seen that normal modes are solutions of the wave function produced by separation of variables. However, when most of authors I've read perform the ...
0
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0answers
18 views

Does logarithmic decrement take into account an increasing period?

I am trying to determine the 'viscous damping coefficient', c, for a mass/Spring system oscillating vertically in water. I was going to use the logarithmic decrement method to determine the damping ...
10
votes
2answers
1k views

How can you make harmonics on a string? [duplicate]

For an oscillating string that is clamped at both ends (I am thinking of a guitar string specifically) there will be a standing wave with specific nodes and anti-nodes at defined $x$ positions. I ...
1
vote
1answer
76 views

Complex resonant frequency not resonant without imaginary part. So can I still just take real part as solution?

I am working with a matrix on a harmonic oscillator problem and the lowest (absolute) frequency $\omega_0$ where the matrix becomes singular is the resonant frequency. Now I obtained this frequency ...
0
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0answers
44 views

About the formula of pendulum simple

for the modulation and the simulation of a pendulum simple , I'm Find this formula : a(t) = a0 * sin ( sqrt(g/l) * t * Pi/2 ) - [ k/(mll) * cos ( sqrt(g/l) * t * Pi/2 ) * t ) ] ...
1
vote
1answer
72 views

How does friction affect the motion of a pendulum?

I would like to know what is the difference in the equation of motion of a pendulum in the presence or the absence of frictional forces. And how this translates to the solution of those equations?
1
vote
1answer
45 views

Are ALL vibrations an exchange of kinetic and potential energy?

I'm taking a course on mechanical vibrational analysis and this is what I was told by my professor, but I'm curious if there are any counter-examples.
3
votes
1answer
72 views

Why is energy in a system typically able to be described using quadratic expressions?

This might be more of an applied math question. Why is the energy of a system typically able to be described using quadratic expressions. Is there an underlying mechanic that drives this?
0
votes
1answer
60 views

How to find when an LRC circuit is critically damped mathematically, given a set of voltage/time data?

In an undergraduate-level experiment to approximate the resistance at which an LRC circuit system is critically damped, I found the resistance range within which the system is likely to be critically ...
0
votes
1answer
39 views

What will happen if you move a photon move in a straight line with no oscillations? [closed]

As light is a wave, it travels in an oscillating pattern: | _ _ _ _ _ _ _ _ |/_\ _ /_\___/_\ _ /_\___/_\ _ /_\___/_\ _ /_\___ | \_/ \_/ \_/ \_/ \_/ \_/ ...
3
votes
3answers
132 views

How can $F_0\cos\omega t$ change to $F_0e^{i\omega t}$ in driven oscillator equation?

I have one thing that confuses me on deriving the solution for the Linear Forced Oscillator. Suppose we have the equation as $$ma + rv + kx = F_0 \cos \omega t$$ What confuses me is when the driving ...
0
votes
0answers
34 views

Pendulum in radial gravity field

All I could find about pendulums assumes that the force on the pendulum mass m is mg directed downwards. The case of m being attracted only by the radial gravity pull (thus replacing the "plane" ...
1
vote
0answers
103 views

Why do trees sway?

Resonance can also occur in three dimensions (such as wind induced swaying) I tried to make a free body diagram (I know it is terribly wrong) to find the forces that causes the tree to undergo ...