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0
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5 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 ...
-1
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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
36 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: ...
0
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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 ...
13
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1answer
143 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 ...
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3answers
26 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
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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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0answers
27 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 ...
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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: $$ ...
1
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1answer
45 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
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1answer
35 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 ...
5
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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 ...
0
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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
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2answers
61 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
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0answers
7 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'}) = ...
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2answers
55 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
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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 ...
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
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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
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3answers
60 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
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
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1answer
65 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?
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1answer
43 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.
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1answer
54 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
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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: | _ _ _ _ _ _ _ _ |/_\ _ /_\___/_\ _ /_\___/_\ _ /_\___/_\ _ /_\___ | \_/ \_/ \_/ \_/ \_/ \_/ ...
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1answer
59 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
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" ...
0
votes
1answer
47 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 ...
2
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1answer
44 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 ...
1
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0answers
89 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 ...
6
votes
2answers
311 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?
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2answers
39 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
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1answer
40 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 ...
3
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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
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2answers
46 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
144 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 ...
0
votes
1answer
41 views

Lagrangian mechanics - small oscillations around equilibrium diagonalization

In my analytical mechanics class, we have been taught that normal modes of small oscillations around equilibrium are given by the solution of $$ p(\omega) = \det(K-\omega^2M) = 0 $$ Where $K_{ij} = ...
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0answers
23 views

Coulomb's static friction in multidimensional case - decide which mass begins to move

Consider a system of N coupled oscillators, under the effect of elastic forces, damping, dynamic and static friction and an external force; for simplicity, let's suppose $N=3$. The friction model is ...
0
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1answer
43 views

Tension in a vibrating loop

Consider a super basic 1D vibrating string, with standing waves on it. The string has length $L$, and the wave propagates at a velocity $v$. The fundamental frequency $f_1$ is given by $$f_1 = ...
0
votes
1answer
36 views

How can I derivate the solution of the under-damped harmonic oscillator?

The equation is $$ m\ddot x =-k x -\gamma x$$ Multiply by $1/m$ we get: $$ \ddot x=-\omega_0^2x - \beta x $$ We use the ansatz $x(t)=e^{\lambda t}$ So for the $\lambda_{1,2}$ we get: $$ ...
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5answers
142 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 ...
3
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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
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2answers
49 views

$Ae^{\mathrm{i}\omega t}$ assumption for oscillating systems (formal & intuitive)

When we obtain a system of ODE's for $n$ masses connected with springs (or otherwise obtained by small amplitudes approximation), the next steps are usually assuming a solution in form $Ae^{i\omega ...
0
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0answers
17 views

Diagonal patterns in a Chladni plate experiment [duplicate]

I am an undergraduate student that's taking physics classes and have been assigned a seminar concerning Chladni figures. I understand the theory behind it, the standing waves in 1D and 2D, Bessel ...
3
votes
1answer
56 views

What is the source of the discrepancy in my period-amplitude graph?

I was taught at school that the formula for period of a pendulum is $T=2\pi \sqrt{\frac{l}{g}}$ Later I found out that this is only an approximation valid for small angles and the accuracy of this ...
1
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1answer
44 views

Oscillating block amplitude change when 2nd mass added [closed]

There is a oscillating block with amplitude $A$ and mass $M$. We add a mass $m$ with zero velocity and vertically.when the block is in this two conditions: ...
1
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2answers
84 views

How can a harmonica make some different sounds?

My first post: I have found an interesting harmonica here. So, I tried to know more about harmonica. And, I have read this article , in which the author doesn't mention the physical calculation, ...
0
votes
1answer
151 views

In an RLC series circuit on resonance, how can the voltages over the capacitor and the inductor be larger than the source voltage?

Consider an RLC circuit in series, of the form If the source drives the circuit in AC at the resonance frequency $\omega =1/\sqrt{LC}$, the peak-to-peak voltages on the capacitor and the inductor, ...