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8
votes
1answer
64 views
+50

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
votes
0answers
9 views

Explain quality factor and bandwidth [duplicate]

Can anyone explain concept of quality factor and bandwidth with a mechanical example?
0
votes
1answer
27 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: ...
2
votes
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
votes
0answers
21 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 ...
1
vote
3answers
24 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 ...
0
votes
1answer
38 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}} ...
8
votes
3answers
17k 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
0answers
26 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
votes
4answers
55 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: $$ ...
6
votes
5answers
138 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
vote
1answer
43 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
34 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
724 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
68 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
205 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
votes
0answers
8 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
1
vote
2answers
58 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 ...
0
votes
0answers
6 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
votes
1answer
222 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
votes
1answer
163 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
votes
2answers
54 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
36 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
56 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
votes
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
55 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
votes
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
64 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
42 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
71 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
53 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
129 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
33 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
87 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 ...
0
votes
1answer
44 views

Finding mass attached to the string

I'm given the following problem: One end of a string with a linear mass density of 7.60* 10^-4 is connected to an oscillator with a frequency of 50.0 Hz. The other end is connected to a hanging ...
0
votes
2answers
23 views

Regarding wave displacement equation [duplicate]

in some textbook i read that one can describe wave displacement by y(t)=Asin(ωt+ϕ) and y(t)=Acos(ωt+ϕ) . i know both these terms are periodic but how one can use any of these equations in numericals ...
0
votes
3answers
433 views

Pendulum's motion is simple harmonic motion

For a pendulum's motion to be simple harmonic motion (S.H.M.) is it necessary for a pendulum to have small amplitude or S.H.M. can be produced at large amplitudes as well? If it is really necessary ...
2
votes
1answer
41 views

Amplitude at successive wavefronts?

Consider spherical waves emanating from a point source initially the amplitude is A, as wave travels forming wavefronts will the amplitude of each point in all the secondary wavelets be the same and ...
6
votes
2answers
310 views

How much upward force due to ground vibrations does the Earth exert on you?

Say you're walking by the highway and you can feel the vibrations of cars moving along. How would you approximate the force that the ground is exerting on your feet due to these vibrations?
0
votes
2answers
38 views

SHM with acceleration at mean position

Suppose we have an equation of motion as $$\frac{d^2x}{dt^2} = -kx + c,$$ then can it be called a SHM? Since acceleration is still proportional to displacement. But then, how will we define the mean ...
0
votes
1answer
39 views

phase difference of two reflected wave

Suppose a tuning fork generates sound waves with a frequency of 100 Hz. The waves travel in opposite directions along a hallway, are reflected by end walls, and return. The hallway is 47.0 m long and ...
1
vote
2answers
120 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 ...
3
votes
1answer
45 views

Free body diagram when forces are not directly in contact with the object

I was trying to use Newton's second law to describe the motion of the following pendulum: However, I was confused as to how to include the spring in Newton's second law. I was able to set up a ...
0
votes
2answers
45 views

Damped sinusoidal motion with initial velocity or acceleration [closed]

I am looking for the equation of damped sinusoidal motion with an initial velocity. For example: a mass is moving by spring1 force. At ...
1
vote
2answers
237 views

Small Oscillations and matrices: suggestion about text

I'm undergraduate and I'm looking for a text about Small Oscillations in which matrices are used. Could you suggest me a book or a PDF file?
1
vote
2answers
126 views

Eigenvalue physical meaning [closed]

What is the physical significance of eigenvalues or eigenvectors?? Please try to explain in very simple language simple harmonic oscillator , potential well could you support your answer by ...
1
vote
2answers
155 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 ...