Oscillation Definition and 769 Threads

Oscillation is the repetitive variation, typically in time, of some measure about a central value (often a point of equilibrium) or between two or more different states. The term vibration is precisely used to describe mechanical oscillation. Familiar examples of oscillation include a swinging pendulum and alternating current.
Oscillations occur not only in mechanical systems but also in dynamic systems in virtually every area of science: for example the beating of the human heart (for circulation), business cycles in economics, predator–prey population cycles in ecology, geothermal geysers in geology, vibration of strings in guitar and other string instruments, periodic firing of nerve cells in the brain, and the periodic swelling of Cepheid variable stars in astronomy.

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  1. G

    Is the phase shift of a tuned mass damper ##\frac{\pi}{2}## or ##\pi##?

    Hi. What is the phase shift of a tuned mass damper with respect to the oscillation of the surrounding structure, such as the big pendulum in Taipei 101? Simple resonance theory would suggest ##\frac{\pi}{2}##, but animations in explanatory videos often depict them in anti-phase, i.e. a phase...
  2. M

    I Laser and excited state linewidths in Rabi oscillations

    Hello! I want to simulate (numerically if analytically is not possible) the behavior of a 2 level system, when driven by a laser (basically transition probability vs laser frequency for fixed pulsed time) accounting for the laser and atomic linewidth (in my case I can assume they are...
  3. N

    Damped harmonic oscillation

  4. K

    Advantages of a cone-shaped spring?

    I'm doing a personal experiment where I take a conical spring (that is, a spring with two different diameters on either end), hang it from the ceiling, and measure the period of oscillation for different masses hanging below the spring. I do this for two different orientations of the spring; one...
  5. Boileddog

    Which Spring Constants to Use for Magnet Oscillation Experiment?

    For my academic research project, I am studying the oscillatory of magnets attached to extension springs. And to have variety of data on different types of oscillation, I'll be using different spring constants as a variable. But in order to get the springs I need to know the dimensions of the...
  6. charie

    Oscillation of free surface of water in parallelepiped container

    [Mentor Note: Two duplicate threads merged...] in container with dimensions L×D, rests water of height H and density ρ. we disturb the water along L dimension, and accept an oscillation is caused on the free surface of the water, which maintains its flatness, so that the central of mass of the...
  7. Slimy0233

    B [SOLVED] Regarding the Superposition of Two Plane Waves

    My professor was teaching me about the superposition of two waves and after this derivation, he marked ##2Acos(\frac{dk}{2}x -\frac{d\omega}{2}t)## as the oscillation part and ##sin (Kx-\omega t)## as the oscillation part, I don't understand why? Any answers regarding this would be considered...
  8. guyvsdcsniper

    Find Universal Gravitational Constant w/ Torsion Balance Timelapse Recording

    I am using pasco's gravitational torsion balance https://www.pasco.com/products/lab-apparatus/fundamental-constants/ap-8215 to find the universal gravitational constant in a lab report. Two large tungsten masses are positioned close to two smaller masses, causing the torsion balance to...
  9. Slimy0233

    I Oscillating charged particles and E.M waves

    If I were to tie a friend of mine adjacent to the oscillating charge and make him oscillate in parallel to my oscillating charged particle such that to him the oscillating particle is at rest, would he observe the generation of electromagnetic waves.
  10. orangephysik

    Damped harmonic oscillation of a swingboat

    Hi, so of course Φ0 = 15° and after solving after solving Φ(t=5*T = 5/f) I found γ = 0.012 I need help with b). If I do 2° = 15° * exp(-0.012t)*cos(2πf*t), I'm not able to find t so I did something else by assuming that the amplitude decreases at a constant rate: After 5*T = 5*1/f = 18.52 s...
  11. Penny57

    Oscillation of bead with gravitating masses

    The relevant equations has been me working out the gravitational potential energy. I was told to take the derivative twice from here, but I do not understand why. It leads into a taylor series expansion, which seems excessive, but I was not informed on any other way to do it. Any advice would be...
  12. D

    Density of cylinder that undergoes vertical oscillation

    I'm not sure where to start...
  13. Y

    Functional representation of the oscillating graph

    Hi; This is in fact not a homework question, but it rather comes out of personal curiosity. If you look at the graph of the two functions in the image attached, what is the simplest functional representation for such a symmetrical pattern?
  14. bobacity

    Solving Simple Oscillation Frequency: A Quick Guide

    I think I can solve the frequency by doing 1/0.400 μs, but I'm not sure.
  15. S

    Omission of parts of equations in solving oscillation questions

    Perhaps that's a very dumb question, but I'm having a hard time to understand why it's possible to omit parts of the equations in solving various problems involving oscillations. Here, for example, the complete equation for acceleration is not used (the part with cosine doesn't appear) and here...
  16. Tanreom

    I How does a screw roll down an inclined plane?

    I was thinking about how various objects would slide down on an inclined plane, and I just couldn't figure this problem out. So let's say I have this screw or cone on its side, on an inclined plane. If friction exists, what would the motion of the screw be as it slides down the inclined plane...
  17. link223

    Oscillation with 2 springs attached to a mass

    How in the world I am supposed to start with this problem? No clue, so can't provide HW solution by any means. regards.
  18. L

    A spring, disk and pulley system

    (a) By setting up a coordinate system with the x-axis pointing to the right and the y-axis pointing downward we have ##\begin{cases}-kx_{eq}+T_1+F_{s}=0\\ -RF_{s}+rT_1=0\\ r_p (T_2-T_1)=0\\ -T_2+mg=0\end{cases}\Rightarrow x_{eq}=\frac{mg}{k}\left(1+\frac{r}{R}\right)## which coincides with the...
  19. Rezex124

    I Damped oscillator with changing mass

    Hello, So about two weeks ago in class we looked at RLC circuits in our E&M course, and short story short... we compared the exchange of energy between the Capacitor and the Inductor (both ideal) to simple harmonic motion. Once the capacitor and inductor are not ideal anymore, we said it's...
  20. J

    How Do Normal Modes of Oscillation Relate to Forces on Masses?

    The first part is trivial not sure where to go on the second part.
  21. J

    B Does Relativistic Speed Affect Mechanical Watch Oscillation?

    Does mechanical watch ticks slower when move fast, due to relativistic effects? To make watch tick slower you must change oscillation of balance wheel inside watch, so if answer is yes, what myster "force" change balance wheel oscillation in mechanical watch to ticks slower?
  22. Stonestreecty

    Heavy Amplifier Circuit Oscillation Happened

    Hi, all I am experimenting with audio amplifiers for a while now. I learned how to do an operational amplifier with discrete components and understand all its section and sub-circuits, recently. Then I decided to just skip the hard part and use operational amplifier and output power stage for an...
  23. strangerep

    A Proof that neutrino flavor oscillation implies nonzero neutrino mass?

    [This is a reference request.] I'm dissatisfied with the "proofs" I've found so far. E.g., in Kayser's review from 2008, in the paragraph following his eq(1.4), he assumes a propagation amplitude Prop##(\nu_i)## of ##\exp(-im_i \tau_i)##, where "##m_i## is the mass of the ##\nu_i## and...
  24. R

    Calculate quality factor of a damped oscillation from a graph

    I'm trying to find the quality factor of a damped system. I know 3 points from the graph, ##(t,x): (\frac{\pi}{120},0.5), (\frac{\pi}{80},0), (\frac{\pi}{16},0)## From this I found that ##T = \frac{\pi}{20}## ##\omega_d = \frac{2\pi}{T} = 40 rad## Then, from the solution ##x(t) = A_0...
  25. L

    Amplitude of oscillation of a mass which is the pivot of a pendulum

    1) By conservation of mechanical energy we have ##m_2gl(1-\cos(\alpha))+m_1gl=\frac{1}{2}m_1v_1^2+\frac{1}{2}m_2v_2^2+m_1gl## and by conservation of linear momentum along the x-axis we have ##m_1v_1+m_2v_2=0## which gives us ##v_2=\sqrt{\frac{2m_1gl(1-\cos(\theta))}{m_1+m_2}}## and...
  26. Ang09

    Moment of Inertia with varying distance from Centre of Mass

    h = d1 + 0.08 d1 = h - 0.08 d2 = h + 0.08 I of the vertical portion = 1/12 m (l^2 + b^2) + md1^2 = 1/12 m (0.28^2 + 0.04^2) + m(h - 0.08)^2 I of the horizontal portion = 1/12 m (l^2 + b^2) + md2^2 = 1/12 m (0.28^2 + 0.04^2) + m(h + 0.08)^2 The moment of inertia for the whole T-shape about...
  27. PHYSICSKOP

    I Undamped driven oscillation — Is there a phase delay?

    I know that there is phase delay in damped driven oscillation but I want to know is there any phase delay in undamped driven oscillation when we apply sinusoidal driving force. When driving force is maximum, displacement is also maximum as well right?
  28. P

    Equations of motion of damped oscillations due to kinetic friction

    Take rightwards as positive. There are 2 equations of motion, depending on whether ##\frac {dx} {dt} ## is positive or not. The 2 equations are: ##m\ddot x = -kx \pm \mu mg## My questions about this system: Is this SHM? Possible method to solve for equation of motion: - Solve the 2nd ODE...
  29. B

    How to solve mass-spring system when affected by torque in a pulley?

  30. H

    What is the angular frequency of oscillation?

    ω^2 - (ωo)^2 = 2 (-630) (0.32) = -403.2 This is what I have now and I stuck here.
  31. H

    Find the eigenvalues of a 3x3 matrix

    Hi, I have a 3 mass system. ##M \neq m## I found the forces and I get the following matrix. I have to find ##\omega_1 , \omega_2, \omega_3## I know I have to find the values of ##\omega## where det(A) = 0, but with a 3x3 matrix it is a nightmare. I can't find the values. I'm wondering if...
  32. K

    Charged particle oscillation about the origin

    Hello! This is probably something simple but I am getting confused about it. Assume we have an electric field along the z axis given by ##E = -kz##, with ##k>0##, so the field on both sides of the xy-plane points towards the origin. Let's say that we have a positively charged ion at the origin...
  33. A

    Oscillation of a drumhead membrane

    My attempt, Considering that it jumps in the maximum compression position: $$\frac{kA^2}{2} = mg(H+A)$$ replacing k / m with w ^ 2 : $$A^2 w^2-2gA-2gH=0$$ Solving the second degree equation: $$A=\frac{2g+\sqrt{4g^2+8gHw^2}}{2w^2}$$ But the answer is...
  34. J

    Damped Oscillation Amplitude Decrease vs. Mass Relationship

    so what I did was e^-(1/10.1)=0.9057 and e^-(1/14.8)=0.93466 Then 0.93466/0.9057 = 1.03198, so the heavier mass dampens 1.03 times more than the lighter mass. If the lighter mass decreases the oscillation to 72.1%, then the heavier mass would be 72.1%*1.03198 = 74.4, but this is wrong. It...
  35. J

    Oscillation Spring Dampening Find Frequency

    So first I found what b/2m is and got 0.287129. Then I found what the sqrt part of the equation was and got 1.128713. Then I added them together to find w. Then I divided by 2pi to find frequency and got 0.255, but the answer is 0.180.
  36. J

    Dampening Oscillation Spring Question

    Since its critically damped that means k/m=(b/2m)^2, which would mean w=ib/2m. So m=ib/w. My issue now is that I need to find work. I could put w back into x(t) to get Ae^((-b/2m)t+phi). I guess I could make this Acos((-b/2m)t+phi)). But I am kinda lost at this point. Sure, I could find the...
  37. H

    Oscillation of a particle on a parabolic surface [equation of motion]

    Hi, I have a particle on a parabolic surface $$y = Ax^2$$ and I have to show that the frequency is $$\omega = \sqrt{2Ag}$$ I don't know how to deal with a parabola. I don't think I can use the polar coordinates like a circle. I don't see how to start this problem and in which coordinates...
  38. H

    B Apparent missing negative phase oscillation energy - where is it?

    When an oscillator produces waves - let's say they are highly focused - that are damped by a second negative phase oscillator, where is the wave energy? The energy in each set of waves must still exist. Has it become hidden?
  39. J

    Harmonic Motion Problem - Finding oscillation of charges in a circuit

    So since V(cap) + V(ind)=0 then Q/C + L dI/dt=0 Now since I=dQ/dt, I can replace dI/dt with d^2Q/dt^2 resulting in Q/C + L d^2Q/dt^2 =0 Now L d^2Q/dt^2 looks like a harmonic motion thing I can solve, where w^2=L. This means I can find w. I get 0.0005385. Now my issue is using this w gives the...
  40. K

    I How do two photons affect Rabi oscillations in a 2-level atomic system?

    Hello! Assuming we have a 2 level system (e.g. an atom with 2 energy levels) and the lifetime of the upper level can be neglected, if we make the atom interact with a laser at a fixed frequency, we would get Rabi oscillations (assume the laser is on resonance). Would we still get Rabi...
  41. J

    Exploring Motion in Physics: Beyond Translation, Rotation, and Oscillation

    In high school I learned about three kinds of motion in classical mechanics - translation, rotation, and oscillation. Are there any other kinds of motion in the physical world?
  42. J

    Find ω, the angular frequency of oscillation of the object

    The hint says to use the moment of inertia of the rod, however i have not covered this on my course and I don't know what it is. After googling moment of inertia of a rod I found that it is a quantity expressing a body's tendency to resist angular acceleration, and for a rod I=1/3ML^2. So...
  43. Peter Jones

    The oscillation of a particle in a special potential field

    I couldn't prove the first one but i tried to find the period F = -dU / dx = - d( U0tan^2( x / a ) ) / dx = - U0 ( ( 2 sec^2( x / a ) tan( x / a ) / a ) with F=d^2x/dt^2, tan(x/a)=x/a we have d^2x/dt^2 + U0 ( ( 2 sec^2( x / a ) ( x / a^2 ) =0 from there i don't know how to handle the...
  44. A

    Physics problem relating to an inclined plane and a spring oscillation

    Hello! So my main and first problem about this question is, I do not know what the problem is about. What I mean by that is, in class we talked about pendulums and are given formulas and assignments regarding pendulums. But this problem here does not seem like it has anything to do with...
  45. e_mts

    Real and Complex representations of an oscillation equation

    I've been trying to continue my education by self-teaching during quarantine (since I can't really go to college right now) with the MIT Opencourseware courses. I landed on one section that's got me stuck for a while which is the second part of this problem (I managed to finish the first part...
  46. K

    What Causes Bubble Oscillation According to Gauss's Law?

    From Gauss's Law give ##E=\dfrac{\sigma}{2\epsilon_0}## ##\therefore P_e=\dfrac{\sigma^2}{2\epsilon_0}## Consider at equilibrium (before bubble being charged) ##P_i=P_0+\dfrac{4S}{R}## Using Newton's 2nd Law ##\Sigma F=m\ddot{R}## Let ##R+\delta R## be the new radius Give (after binomial...
  47. LCSphysicist

    What is the Period of Oscillation for a Spring Cut to One-Third Its Length?

    I am not sure if i get the problem, but if i understand, we want to know the period of oscillations on a spring with length l/3. If is this the right interpretation, i would say that the stiffness of the new the spring is k/n, where k is the stiffness of the former spring. This based on the...
  48. Helena Wells

    I Possibilty of flavor oscillation of an electron

    Neutrinos oscillate at different flavors while propagating in space and this is due to their mass.Any particle being massless cannot oscillate between different flavors while leptons with the mass of the electron and above are very unlikely to change their flavor. Will we able to detect a change...
  49. J

    Calculating the amplitude of waves in water

    Suppose I have a perfectly circular pool which is four meters in radius, two meters in depth, and filled with water. Say I drop a steel ball with a radius of five centimeters into the middle of the pool from a height of five meters above the water's surface. After three seconds, what will be the...
  50. dRic2

    I Phonon Number Conservation in a Single Mode Oscillation Experiment

    Suppose I prepare an experiment where I excite a single mode of oscillation of the lattice, that is something like ##u(x, t) = Ae^{i(kx-\omega t)} ## (in the classical limit). The energy corresponding to that mode should be ##E = \frac 1 2 \rho L^3 A^2 \omega^2 ##. If I equate this equation to...
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