What is Oscillation: Definition and 766 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. Kaushik

    B Forced Oscillations: Pendulum 1 Driving Neighboring Pendulum

    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...
  2. Beelzedad

    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...
  3. F

    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...
  4. 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...
  5. Saptarshi Sarkar

    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.
  6. Saptarshi Sarkar

    Time period of oscillation of charge in front of infinite charged plane

    I tried to calculate the time the charged particle will take to reach the plane using the a and using d=1/2at² and found the t to be equal to root(4εmd/σq). I guess the time period of oscillation will be double of t (by symmetry), i.e. 2root(4εmd/σq). I don't know if this is correct.
  7. ContagiousKnowledge

    General solution of the spherical wave equation

    Since the spherical wave equation is linear, the general solution is a summation of all normal modes. To find the particular solution for a given value of i, we can try using the method of separation of variables. $$ ψ(r,t)=R(r)T(t)ψ(r,t)=R(r)T(t) $$ Plug this separable solution into the...
  8. ContagiousKnowledge

    Normal modes of a rectangular elastic membrane

    Let's try inputting a solution of the following form into the two-dimensional wave equation: $$ \psi(x, y, t) = X(x)Y(y)T(t) $$ Solving using the method of separation of variables yields $$ \frac {v^2} {X(x)} \frac {\partial^2 X(x)} {\partial x^2} + \frac {v^2} {Y(y)} \frac {\partial^2 Y(y)}...
  9. U

    Derivation of the oscillation period for a vertical mass-spring system

    I understand the derivation of T= 2π√m/k is a= -kx/m, in a mass spring system horizonatally on a smooth plane, as this equated to the general equation of acceleration of simple harmonic motion , a= - 4π^2 (1/T^2) x but surely when in a vertical system , taking downwards as -ve, ma = kx - mg...
  10. bubble-flow

    Oscillation of a particle inside water caused by a sound wave

    I don't really know where to start as this is not exactly my homework and I finished school some 15 years ago. I looked into my old high school notes, the last time I ever had anything about mechanical waves and sound. Unfortunately, we never learned anything about sound waves causing...
  11. person123

    I Find Frequency of Block Oscillation Due to Shear Force

    Hi. I'm trying to determine the frequency of an block (roughly a rectangular prism) when the oscillation is due to a shear restoring force. Here is a diagram: In the derivation, ##\rho## is the density of the block,##G## is the shear modulus of the block, ##y## is the elevation of the element...
  12. A

    Finding the Position(s) of Particle Oscillation

    My first impression was that since the external force was constant it wouldn't make any change on the period of oscillation of the system. But on further thinking I found that if I were to only consider the one dimensional oscillation of the particle then the component of force along the string...
  13. D

    How to find the period of small oscillations given the potential?

    I first found the equilibrium points taking the derivative of the potential. ##U'(x)=U_0 a\sin(ax)##, and the equilibrum is when the derivative is 0, so ##U_0 a\sin(ax)=0## so ##x=0## or ##x=\pi/a##. Taking the second derivative ##U''(x)=U_0a^2 \cos(ax)## I find that ##x=0## is a minimum point...
  14. A

    I Is this allowed? - Harmonic oscillation

    I divide by zero which is a no-go, but on the other hand: at resonance frequency the phase-shift is 90 degrees.
  15. A

    Is this an allowed solution? - 2nd order harmonic oscillation

    It is true that at resonance frequency the phase-shift between input and output is 90 degrees, so my mind would think that this is ok. But I am kind of unsure because of the whole dividing by zero part. If this isn't allowed: is there any way to calculate/measure the damping coefficient with...
  16. Protea Grandiceps

    I X variable in damping force equation for damped oscillation?

    Hi, for ease of reference this posting is segmented into : 1. Background 2. Focus 3. Question 1. Background: Regarding (one, linear, second-order, homogeneous, ordinary, differential) equation describing the force in a non-driven, damped oscillation: F = m.a = -k.x - b.v F =...
  17. Miles123K

    Normal mode of an infinite spring pendulum system

    First I worked out the dispersion relations, which is pretty easy: ##M \ddot x_j = K x_{j-1} + K x_{j+1} - 2K x_j -mg \frac {x_j} {l} ## (All t-derivatives) We know ##x_j## will be in the form ##Ae^{ijka}e^{-i\omega t}## so the above becomes: ## -\omega^2M = K (e^{-ika}+e^{ika}-2)-\frac {g}...
  18. VicomteDeLaFere

    I Oscillation with constrained amplitude

    Hello, Suppose we have a simple oscillating spring mass system. The natural frequency will excite the system to have infinite amplitude. Suppose then, that we have that system on a table so that amplitude is limited. I'm imagining the high school experiment with the spring mass system on the...
  19. Danny Boy

    Approximate solutions to Kuramoto synchronization model

    According to the wiki entry 'Kuramoto Model', if we consider the ##N=2## case then the governing equations are $$\frac{d \theta_1}{dt} = \omega_i + \frac{K}{2}\sin(\theta_2 - \theta_1)~~~\text{and}~~~\frac{d \theta_2}{dt} = \omega_i + \frac{K}{2}\sin(\theta_1 - \theta_2),$$ where ##\theta_i##...
  20. Miles123K

    Oscillation of a driven RLC network

    We know that the charge on capacitors as a function of time takes the general form of: ##Q(x,t)=qe^{ijka}e^{-i\omega t}## The voltage at each capacitor: ##V_j = \frac 1 C (Q_j-Q_{i+1})## From KVL we have differential equation of t-derivatives: ##LQ'' + RQ' = V_{j-1} - V_{j}## ##LQ''+RQ'= \frac...
  21. PhysicS FAN

    How can I solve for the sines and cosines in a harmonic oscillation problem?

    First of all, I found a function of the distance of the object form the equivalence point in both cases. I got something like d=2d' where d is the distance at the first case and d' at the second. I did that because I wanted to find the frequency, and so first I need to find the period of...
  22. Miles123K

    Force and power applied to create a traveling wave

    Again I am really confused, but I just put the traveling wave as: ##\psi(x,t) = Dcos(kx- \omega t)## for positive x ##\psi(x,t) = Dcos(kx+ \omega t)## for positive x Then I simply differentiated and plugged in ##x=0## ##F(t) = - T D k sin(\omega t)## and from this ## \langle P \rangle = T D^2 k...
  23. J

    Looking for some help realting to spring energy changes

    Homework Statement https://imgur.com/gallery/PQx8SmXHomework Equations EPE (elastic potential energy) = 1/2kx^2 GPE (gravitational potential energy) = mgh The Attempt at a Solution my attempt, https://imgur.com/gallery/lJDhwqD [/B] I feel like I've made progress considering the quadratic...
  24. osten

    Oscillation Problem -- Ball mass on the end of a horizontal spring

    Homework Statement A 200 g ball attached to a spring with spring constant 2.40 N/m oscillates horizontally on a frictionless table. Its velocity is 20.0 cm/s when x=−5.00cm. What is the amplitude of oscillation? Homework Equations f=√(k/m) /2π x(t) = Acos(2πft) v(t) = -2πfAsin(2πft) The...
  25. Another

    Forced Oscillation: Understanding Force & Mass

    I don't understand. Why don't have ##mg## force action on this mass. Please explain this problem to me.
  26. M

    Solve Harmonic Oscillation Homework: E, F, T, ƒ

    Homework Statement Harmonically fluctuating object. It`s full energy (E) is 3*10-5 J. Maximum force (F) on object is 1.5 * 10-3N. Period is 2 seconds (T) and starting phase (ƒ) is 60°. Need to write equation for these fluctuations. E = 3*10-5 J F= 1.5 * 10-3N T = 2 s ƒ = 60° Homework Equations...
  27. Kkurenai

    Need help to solve an oscillation problem.

    Homework Statement It's an oscillation problem. I have to find the FIRST time when the spring-mass system will have E (mechanical energy) = K (kinetic energy), if x(t)=12sin(5t+3,5). (t is time in seconds, x is lenghtof the system in cm). Homework Equations E=1/2kA^2 K= 1/2kx^2 The Attempt...
  28. T

    Simple harmonic motion equation

    Homework Statement Calculate the harmonic motion equation for the following case A=0.1m, t=0s x=0.05m, v(t=0)>0 a(t=0)= -0.8m/s^2 Homework Equations x(t)= +/-Acos/sin ( (2pi/T)/*t) The Attempt at a Solution [/B] A is given to be 0.1 so I simply place it into the equation. Now I have to...
  29. navneet9431

    Is it possible to apply energy conservation here?

    Homework Statement Homework Equations Kinetic Energy =1/2*m*v^2 Spring Potential Energy = 1/2*k*x^2 Gravitational Potential Energy = m*g*h The Attempt at a Solution I am thinking to solve this problem using energy conservation but I feel that it is not possible to apply energy conservation...
  30. J

    Determine the period of small oscillations

    Homework Statement Two balls of mass m are attached to ends of two, weigthless metal rods (lengths l1 and l2). They are connected by another metal bar. Determine period of small oscillations of the system Homework Equations Ek=mv2/2 v=dx/dt Conversation of energy 2πsqrt(M/k) The Attempt at a...
  31. J

    Small oscillation frequency of rod and disk pendulum

    Homework Statement Consider a rod of length ##L## and mass ##M## attached on one end to the ceiling and on the other end to the edge of a disk of radius ##r## and mass ##m##. This system is slightly moved away from the vertical and let go. Let ##\theta## be the angle the pendulum makes with the...
  32. Beth N

    Driven Oscillation: Springboard diving

    Homework Statement A light springboard deflects 15cm when a 65kg diver stands on its end. He jumps up and down, depressing it by 25 cm, then he moves up and down with the oscillations of the end of the board. What is the amplitude of the oscillation when the diver just become airborne? What is...
  33. Zack K

    Dimensional Analysis of an oscillation

    Homework Statement The period of oscillation of a nonlinear oscillator depends on the mass m, with dimensions M; a restoring force constant k with dimensions of ML-2T-2, and the Amplitude A, with dimensions L. Use dimensional analysis to show what the period of oscillation would be proportional...
  34. K

    I Phase angle of a damped driven harmonic oscillation

    Hello, in every book and on every website (e.g. here http://farside.ph.utexas.edu/teaching/315/Waves/node13.html) i found for driven harmonic osciallation the same solution for phase angle:θ=atan(ωb/(k−mω^2)) where ω is driven freq., m is mass, k is spring constant. I agree with it =it follows...
  35. K

    B LC Oscillation: Current Flow & Charge Polarity

    when in LC oscillation current flow from inductance to capacitor and charge is opposite polarity. why don't current flow in reverse of it and charging the capacitor in same manner as it was earlier.
  36. Safder Aree

    Simple Pendulum undergoing harmonic oscillation

    Homework Statement Is the time average of the tension in the string of the pendulum larger or smaller than mg? By how much? Homework Equations $$F = -mgsin\theta $$ $$T = mgcos\theta $$ The Attempt at a Solution I'm mostly confused by what it means by time average. However from my...
  37. Mzzed

    Creating oscillations on the output of a DC power supply

    Is there some common parameter for DC power supplies that provides the maximum oscillation amplitude allowable at the output? For some context - I would like to generate an oscillating signal powered by a DC power supply, but to prevent most of the oscillations reaching the DC supply I am going...
  38. J

    I Neutrino masses and oscillation

    <Moderator's note: Spin-off from another thread: https://www.physicsforums.com/threads/does-red-shift-approach-infinite-near-time-zero.948696/.> We do, however, have a lower limit, because of the solar neutrino experiment: too light and the neutrinos wouldn't have enough proper time to...
  39. U

    I Circular orbit + small radial oscillation about circular orbit

    The potential energy of a particle of mass $m$ is $U(r)= k/r + c/3r^3$ where $k<0$ and $c$ is very small. Find the angular velocity $\omega$ in a circular orbit about this orbit and the angular frequency $\omega'$ of small radial oscillation about this circular orbit. Hence show that a nearly...
  40. B

    Proof of oscillation about the equilibrium

    Homework Statement The problem is question 2(a) in the attached pdf. I seem to find myself at a dead end and am not sure where to go from here - I will attach my working in a separate file, but basically I need to show that the oscillator passes/crosses over the x = 0 boundary at a positive...
  41. K

    I Neutrino Mass: Exploring the Oscillation Phenomenon

    Why is there an assumption that if neutrinos didn't have mass they would move at the speed of light? and how does the fact they oscillate prove they have mass?
  42. Ari

    How to find period of a SHM concerning a cube and spring?

    1. Homework Statement The 4.00 kg cube in the figure has edge lengths d = 8.00 cm and is mounted on an axle through its center. A spring ( k = 1400 N/m ) connects the cube's upper corner to a rigid wall. Initially the spring is at its rest length. If the cube is rotated 4.00° and released, what...
  43. I

    Ball suspended by a pulley: oscillation

    A ball of 100g, suspended from a pulley of a dynamometer, oscillates freely. The length of the pendulum thus obtained is 1m. What are the indications of the dynamometer when the ball is at the point A of it's trajectory? The maximum offset angle is 15 degrees. Homework Equations α - alpha...
  44. Phantoful

    Max ω of circular hoop rotating around a peg and oscillation

    Homework Statement Homework Equations F=ma τ = Iα = rF v=rω, a=rα L = Iω Center of Mass/Moment of intertia equations The Attempt at a Solution [/B] So right now I've tried to model the force acting on the ring as it goes around the peg, but I think centripetal force is involved and I'm not...
  45. Soffie

    The period of oscillation of a bob in an accelerating frame

    If a suspended pendulum bob is accelerated (in a car, for example), if you're in the accelerating frame of reference, you will observe the fictitious force which appears to act on the bob (as you're in the accelerating frame, the bob is not 'moving' so to speak, so to establish equilibrium you...
  46. K

    Solving Harmonic Oscillation w/ BC y(1)=B

    Homework Statement [/B] For differential equation of the form ## y''- y = 0 ## BC is ## y(1) = B ## which usually have general solution ## y(x) = C1 e^x + C2 e^{-x} ## But this manual I am reading always want to go with general solution ## y = C1 \cosh(x) + C2 \sinh( x) ## I assume...
  47. another_dude

    B Formula of S in simple harmonic oscillation

    In school we have numerous exercises that ask you to find the time when a body passes a certain point for the nth time in simple harmonic oscillation. But it is a bit mentally taxing to solve with the actual formula of x=Asin(ωt + φ), just because you have to sort out all the infinite solutions...
  48. entropy1

    B Oscillations in a driven spring

    If I have a spring with resonance frequency fres and I drive it with frequency fdrive, the spring will oscillate in a superposition of two frequencies, right? Which frequencies are they?
  49. R

    Oscillation of a bound particle in a superposition of states

    Homework Statement A bound particle is in a superposition state: \psi(x)=a[\varphi_1(x)e^{-i\omega_1t}+\varphi_2(x)e^{-i\omega_2t}] Calculate <x> and show that the position oscillates. Homework Equations <x>=\int_{-\infty}^{\infty} \psi(x) x \psi^*(x) \mathrm{d}x The Attempt at a...
  50. M

    A What are the oscillation modes in low-gravity capillary-dominated flow?

    Hi PF! I am solving a problem for low-gravity capillary-dominated flow, where liquid rests in a rectangular (2D) channel. The text I'm reading introduces a velocity potential ##\hat u = \nabla \phi##, and then states that each oscillation mode is ##\partial_n\phi|_\Gamma = \nabla \phi \cdot...
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