# What is Oscillation: Definition and 761 Discussions

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. ### 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.
2. ### 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...
3. ### 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...
4. ### Density of cylinder that undergoes vertical oscillation

I'm not sure where to start...
5. ### 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?
6. ### Simple Oscillation Question

I think I can solve the frequency by doing 1/0.400 μs, but I'm not sure.
7. ### 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...
8. ### 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...
9. ### 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.
10. ### 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...
11. ### 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...
12. ### Normal modes of oscillation

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

### B How do relativistic effects change oscillation of the balance wheel in mechanical watch causing it to tick slower?

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?
14. ### 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...
15. ### 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...
16. ### 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...
17. ### 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...
18. ### 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...
19. ### 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?
20. ### 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...

22. ### 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.
23. ### 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...
24. ### 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...
25. ### 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...
26. ### 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...
27. ### 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.
28. ### 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...
29. ### 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...
30. ### 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?
31. ### 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...
32. ### I Two photon Rabi oscillation

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...
33. ### 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?
34. ### 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...
35. ### 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...
36. ### 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...
37. ### 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...
38. ### Charged Bubble Oscillation

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...
39. ### Oscillation of a cutted spring

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...
40. ### 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...
41. ### 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...
42. ### 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...
43. ### Oscillation of a boat in still water (Metacenter and Center of Mass)

Let’s say we have a boat whose longitudinal axis is the y-axis (which goes into the screen in the figure below) standing upright in a still water . ##S## is the Center of Mass of the boat and ##C## is the Center of Mass of the displaced water.On ##S## lies the force ##\mathbf W##...
44. ### The periodic time of an elastic string's oscillation

i guess he is asking for the periodic time : $$Tension = \frac {λ*y}{a}$$ $$\lambda= mg$$ $$y =3a$$ $$T = 3mg$$ $$F = T-mg\Longrightarrow F = 3mg-mg = 2mg$$ $$m{y}''=2mg$$ $$y'' = 2g \therefore\frac { dy'}{dt} = 2g \Longrightarrow y' = 2gt+c1$$ by applying the boundary conditions and...
45. ### B Do fluid oscillation characteristics depend on the viscosity of a fluid?

This is my first thread here, so let me know if I didn't adhere to a format i was to follow. I'm in the middle of a project depicting the change that an oscillation of fluid inside a drinking straw faces depending on the viscosity of the liquid. For reference, this is exactly the same example...
46. ### B Forced Oscillations

Consider the following setup: In this, let us set the pendulum 1 into motion. The energy gets transferred through the connecting rod and the other pendulum starts oscillating due to the driving force provided by the oscillating pendulum 1. Isn't it? So the neighbouring pendulum starts...
47. ### How to know whether motion is simple harmonic motion or not?

I am reading "Coulomb and the evolution of physics and engineering in eighteenth-century France". There it is said in page 152 para 1 that "Coulomb found that within a very wide range, the torsion device oscillated in SHM". My questions are: (1) By just looking at the time period of the...
48. ### How does ultrasonic oscillation reduce sliding friction?

Hi everyone! Sorry if I'm not able to work through this problem very much myself... I'm a Food Science student, and I'm trying to read an article about ultrasonic cutting when applied to apple slicing. From the papers they reference, the rapid vibrations on the blade reduce the friction...
49. M

### Oscillation frequency of 2D circular drop in an ambient environment

Hi PF! Do you know what the natural oscillating frequencies are for a 2D circular drop of liquid in an ambient environment (negligible effects)? Prosperetti 1979 predicts the frequencies for both a spherical drop and bubble here at equations 5b and 6b. There must be a simpler circular 2D...
50. ### Amplitude of oscillation for SHM

From the first part of the question, I was able to get the value of ω which will be the same for the next SHM. But, I am having difficulties solving for the amplitude as I can't find the boundary conditions required to get the amplitude.