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-4
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1answer
24 views

Oscillation of a simple pendulum [on hold]

What is maximum possible time period of oscillation of a simple pendulum on earth? Please elaborate your answers.
-1
votes
1answer
43 views

Is this differential equation (for damped & driven physical pendulum) physically valid?

Following is the equation of motion for a physical pendulum which is damped and driven by a force of frequency $f$: $$\frac{d^2 \theta}{dt^2} + b \frac{d\theta}{dt} + sin(\theta) = Tsin(2\pi ft)$$ ...
1
vote
2answers
123 views

Special Relativity - oscillator paradox

I am reading about the Special relativity and the original Einstein papers from 1905 and 1920 where he derives the Lorentz transformation and the effects of the time dilation and space contraction ...
-1
votes
0answers
27 views

Carbon dioxide oscillations along main axis ---TRICKY PROBLEM— [closed]

I'm completely new to physics.stackexchange.com. I would like to try this kind of service. I have received a problem from my professor which sounds like this : "Carbon dioxide molecule in ...
1
vote
1answer
58 views

Finding resonant amplitude [closed]

For a system of oscillations described by the differential equation: $$ \cfrac{d^2x}{dt^2} -\epsilon \cfrac{dx}{dt} + x = \cos(\omega t)$$ We find that the response amplitude $R(\omega)$ to be: ...
0
votes
0answers
18 views

Relation between Qualiy factor and FWHM

I know how to show that the Quality factor $Q=\omega/\nu$ of a damped harmonic oscillator (for example like in this link: http://farside.ph.utexas.edu/teaching/315/Waves/node11.html). What I don't ...
1
vote
4answers
42 views

Pendulum and simple harmonic motion

I have a physical pendulum that, for small oscillations, can be modeled with the simple harmonic motion approach. In determining the motion equation, I need to figure out the amplitude: I know that ...
-1
votes
3answers
94 views

Why does the period of a pendulum decrease in an accelerating frame? [duplicate]

If there is a simple pendulum in a non-accelerating frame with period $T_1$, it will have period $T_2 < T_1$ when placed in a frame accelerating perpendicularly to the direction of gravity. Why?
0
votes
2answers
40 views

Independence of Period and Amplitude in Simple Harmonic Motion

In Simple Harmonic Motion, the period $T$ of an oscillation, is said to be independent of the amplitude $A$ of an oscillation, but why is that so? Attempting to derive from the equations of Simple ...
1
vote
2answers
33 views

How do I draw the force field lines of an isotropic oscillator?

In general, how do I draw the force field lines (in the sense of Faraday, i.e. continuous curves whose tangents give the directions and the density of lines give the intensity of the field) of a ...
0
votes
2answers
41 views

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

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
votes
0answers
26 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
votes
1answer
46 views

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

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 ...
1
vote
1answer
90 views

Period of a pendulum [closed]

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: $$\...
0
votes
2answers
42 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
0answers
17 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 ...
0
votes
1answer
45 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 x(...
0
votes
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 w(x,t)}{\...
0
votes
1answer
40 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
votes
0answers
26 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
votes
2answers
178 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
3answers
34 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
45 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}} u(x+...
0
votes
0answers
29 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
59 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
vote
1answer
49 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
31 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
44 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
votes
0answers
71 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
votes
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
1
vote
2answers
83 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
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'}) = \frac{1}{T}...
0
votes
2answers
58 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
1answer
47 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
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
3answers
65 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
47 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
76 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
47 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.
0
votes
1answer
81 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: | _ _ _ _ _ _ _ _ |/_\ _ /_\___/_\ _ /_\___/_\ _ /_\___/_\ _ /_\___ | \_/ \_/ \_/ \_/ \_/ \_/ ...
1
vote
1answer
86 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
35 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
57 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
26 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 ...
3
votes
1answer
53 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
vote
0answers
125 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
320 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?