Oscillations Definition and 518 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. 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...
  2. sergiokapone

    B Is the Motion of a Pendulum Described by a Harmonic Oscillator Model?

    It is necessary to make a mechanism, the basis of which should be oscillation of the pendulum with an amplitude φ = 0.250 ± 0.002 rad. Is it possible to describe the motion of the pendulum to use a harmonic oscillator model?
  3. sdefresco

    Misc. Analyzing Oscillations of a Metal Semi-cylinder

    I want to replicate the rocking semi-cylinder problem from analytic mechanics, but don't actually have in my possession a nice, solid cylinder to rock. I imagine my professor likely made his, or found it somewhere in Estonia. If anyone can point me to place where I might be able to find one for...
  4. D

    A position of stable equilibrium, and the period of small oscillations

    I tried by taking the derivative of the potential to find the critic points and the I took the second derivative to find which of those points are minimum points. I found that the point is ##x=- a##. I don't understand how to calculate the period, since I haven't seen anything about the harmonic...
  5. D

    Equation of motion for oscillations about a stable orbit

    Homework Statement A) By examining the effective potential energy find the radius at which a planet with angular momentum L can orbit the sun in a circular orbit with fixed r (I have done this already) B) Show that the orbit is stable in the sense that a small radial nudge will cause only...
  6. R

    I Damped Oscillations: Does a Pendulum Ever Truly Stop?

    A pendulum with no friction/resistance/damping (i.e. in a vacuum) will swing indefinitely. Does a pendulum with damping effects ever truly stop oscillating? That is, does the graph tend to infinity or actually reach a value of 0, i.e. the equilibrium position? Thanks for your time.
  7. C

    Find the period of small oscillations (Pendulum, springs)

    Homework Statement A uniform rod of mass M, and length L swings as a pendulum with two horizontal springs of negligible mass and constants k1 and k2 at the bottom end as shown in the figure. Both springs are relaxed when the when the rod is vertical. What is the period T of small oscillations...
  8. D

    Period of Oscillations near equator

    Homework Statement A bead slides along a frictionless wire which lies in the N/S direction, midpoint at the equator. All points along the wire are the same distance from the center of the earth. The bead is initially at rest then released a small distance, δ, to the north of the equator...
  9. A

    Angular frequency of the small oscillations of a pendulum

    Homework Statement One silly thing may be I am missing for small oscillations of a pendulum the potential energy is -mglcosθ ,for θ=0 is the point of stable equilibrium (e.g minimum potential energy) .Homework Equations Small oscillations angular frequency ω=√(d2Veffect./mdθ2) about stable...
  10. U

    How Do You Calculate the Natural Angular Frequency of a Dual-Spring System?

    Homework Statement The suspension of a modified baby bouncer is modeled by a model spring AP with stiffness k1 and a model damper BP with damping coefficient r. The seat is tethered to the ground, and this tether is modeled by a second model spring PC with stiffness k2. The bouncer is...
  11. L

    Modeling the Driven Damped Oscillations in a Material

    Homework Statement [/B] Let us assume that neutral atoms or molecules can be modeled as harmonic oscillators in some cases. Then, the equation of the displacement between nucleus and electron cloud can be written as $$\mu\left(\frac{d^x}{dt^2}+\gamma\frac{dx}{dt}+\omega_0^2x\right)=qE.$$ where...
  12. C

    Spring with oscillating support (Goldstein problem 11.2)

    Homework Statement A point mass m hangs at one end of a vertically hung hooke-like spring of force constant k. The other end of the spring is oscillated up and down according to ##z=a\cos(w_1t)##. By treating a as a small quantity, obtain a first-order solution to the motion of m in time...
  13. 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...
  14. CMJ96

    Understanding Josephson Oscillations: Solving for the Second Derivative of Theta

    Homework Statement [/B] Homework Equations Sorry about this, I had to put this into wolfram alpha as for some reason it would not work in latex The Attempt at a Solution Assuming Ec and Ej are not dependant on time, I have differentiated the first term in equation 10 with respect to...
  15. thebosonbreaker

    Simple Harmonic Motion: why sin(wt) instead of sin(t)?

    Hello, I have recently been introduced to the topic of simple harmonic motion for the first time (I'm currently an A-level physics student). I feel that I have understood the fundamental ideas behind SHM very well. However, I have one question which has been bugging me and I can't seem to find a...
  16. S

    How Do You Calculate Oscillation Frequency for a Quadratic-Cubic Potential?

    Homework Statement A particle moves in 1D in a potential of the form $$U=Ax^2+Bx^4$$ where A can be either positive or negative. Find the equilibrium points and the frequency of small oscillations. Homework EquationsThe Attempt at a Solution So the equilibrium points are obtained by setting...
  17. 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...
  18. R

    Oscillations of Spring with Viscous Medium

    Homework Statement A spring with K=12N/m and an attached bob oscillates in a viscous medium.Amplitude is 6cm from equilibrium position at 1.5 s and Next amplitude of 5.6 cm occurs at 2.5s. what is its displacement at 3s and 4.5s and t=0s Homework Equations x(t)=Xme^-bt/2m The Attempt at a...
  19. ShayanJ

    A Problem with neutrino oscillations

    The phenomena of neutrino oscillations (as I understand it) is based on the idea that neutrino mass eigenstates are not the same as the flavor eigenstates and being in a definite mass eigenstate means the paticle has no definite flavor and vice versa. But this doesn't make sense to me, because...
  20. 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?
  21. F

    I Exploring Oscillations & Interference in Particle Physics

    I will soon start with the course introduction to QFT and are hence an amateur on the subject. However I could not help but wonder, If particles are describes by oschlliations in a field, how can a "bigger body" be made up of several such oscillation? (A bigger particle is made out of several...
  22. J

    I What are the differences between photon and neutrino oscillations?

    i'm wondering about the differences in oscillations between a photon and neutrino, does a neutrino have a wider probability range (or a greater amplitude for a possible location than does a photon) how do the probability ranges for a photon and a neutrino compare when not looking at wavelength...
  23. M

    I Atomic Oscillations & Redshift in Sun and Earth

    My question is very simple (and I assume it has been discussed before but I cant't find the topic): An atom in the Sun emits a photon detected by an observer on Earth. Disregarding uncertainties and experimental problems relating to the movement of the atom (or assuming we could correct for...
  24. AbigailG

    Find an Expression for the Frequency - Pendulum

    Homework Statement [/B] A solid sphere of mass M and radius R is suspended from a thin rod. The sphere can swing back and forth at the bottom of the rod. Find an expression for the frequency of small angle oscillations.Homework Equations f = 1/2(pi) sqrt(MgR/I) I for a solid sphere 2/5MR^2The...
  25. Aboramou

    Calculating Clicks: Spoke Card Oscillations and Rotational Motion

    Homework Statement A thin card produces a musical note when it is held lightly against the spokes of a rotating wheel. If the wheel has 32 spokes, how quickly must it rotate, in revolutions per minute, in order to produce the A above middle C (i.e. 440 Hz)? Homework Equations ω=2πƒ; ƒ=1/T...
  26. peadar2211

    Determine the stability of a fixed point of oscillations

    Homework Statement I have a system of coupled differential equations representing chemical reactions and given certain initial conditions for the equations I can observe oscillation behaviour when I solved the equations numerically using Euler's Method. However, then it asks to investigate the...
  27. J

    A What is the method for calculating the dampening of thermal oscillations?

    Hello, I am attempting to solve the 1 d heat equation using separation of variables. 1d heat equation: ##\frac{\partial T}{\partial t} = \alpha \frac{\partial^2 T}{\partial x^2}## I used the standard separation of variables to get a solution. Without including boundary conditions right now...
  28. S

    Small oscillations and a time dependent electric field

    Homework Statement [/B] Here's the problem from the homework. I've called the initial positions in order as 0, l, and 2l. Homework Equations The most important equation here would have to be |V - w2*M| = 0, where V is the matrix detailing the potential of the system and M as the "masses" of...
  29. W

    Complex Solutions to Oscillations

    Homework Statement Homework EquationsThe Attempt at a Solution I tried differentiating both sides of 3 and re-arranging it such that it started to look like equation 2, however i got stuck with 2 first order terms z' and couldn't find a way to manipulate it into a function z. I then tried...
  30. P

    Lagrangian rolling cylinders + small oscillations

    Homework Statement A point mass m is fixed inside a hollow cylinder of radius R, mass M and moment of inertia I = MR^2. The cylinder rolls without slipping i) express the position (x2, y2) of the point mass in terms of the cylinders centre x. Choose x = 0 to be when the point mass is at the...
  31. J

    Oscillations and harmonics issues for components

    Is there a book/report(s) that can shed light on this issue? I am into making custom projects that are powered by engines and one, in particular, I am very interested in making sure I don't get any induced vibrations or oscillations. Suppose I have my engine affixed to a frame and I wish to...
  32. S

    Time period of small oscillations of the point dipole

    Homework Statement In an infinite flat layer of thickness 2d, volume charge density is given according to the law: ρ=(ρ°)(x)/d and (-d≤x≤d). Here, x is the axis perpendicular to the plane. In the layer, there is a thin channel in which a point dipole of mass m and dipole moment p is placed...
  33. G

    Damped oscillation of a car on a road: velocity calculation

    Homework Statement The car circulates on a section of road whose profile can be approximated by a sinusoidal curve with the wavelength of 5.0 m. The mass of the car is 600.0 kg, and each wheel is equipped with a constant spring k = 5000 Nm-1 and a damper with constant b = 450 Nm-1s. Calculate...
  34. zwierz

    Small oscillations in nonholonomic systems

    I wonder why nobody discuss this topic in classical mech. courses
  35. TheBigDig

    Resistance of an oscillating system

    Homework Statement [/B]Homework Equations ##F = -kx = m\ddot{x} ## ## f = \frac{2\pi}{\omega}## ## \omega = \sqrt{\frac{k}{m}} ## ##\ddot{x} + \gamma \dot{x}+\omega_o^2x = 0 ## ##\gamma = \frac{b}{m}## The Attempt at a Solution I'm stuck on part c of this question. Using the above equations I...
  36. baldbrain

    How do I use the number of oscillations given?

    Homework Statement The length of a simple pendulum is about 100 cm known to have an accuracy of 1 mm. Its period of oscillation is 2 s determined by measuring the time for 100 oscillations using a clock of 0.1 s resolution. What is the accuracy in the determined value of g? (a) 0.2%...
  37. T

    I Resonant, non resonant neutrino oscillations and Dark Matter

    Hello I am aware that one method behind the production of right handed neutrinos is neutrino oscillation. Its been theorized that both non resonant and resonant neutrino oscillation can produce them I know that with non resonant neutrino oscillation the neutrinos don't reach thermal...
  38. T

    I Neutrino Oscillations and Mass

    Hello Just wondering, would neutrino oscillations occur is the three standard model neutrinos were the same mass? or are different masses needed in order to have different phases differences, as the phases differences are why the oscillations occur?Also why do neutrino oscillations prove that...
  39. M

    Analysing short period oscillations of an aircraft

    Homework Statement Recently did a lab experiment were 3 different flight conditions were applied to the same aircraft to see how it affected the aircraft dynamics, we analysed the results by two different methods 1.) calculate using the flight coniditons with a formula sheet and 2.) we printed...
  40. M

    Short-period oscillations in different flight conditions

    Homework Statement In a lab experiment we ran the simulation of 3 different flight conditions into a program that produced graphs of the oscillations in them conditions and we have to do a comparison of the SPO (short period oscillations) characteristics for the 3 flight conditions which are...
  41. J

    Spring set makes up a traveling wave

    Homework Statement Twelve identical mass-spring combos are lined up and set to oscillation. Two pictures of the same system taken at different times are shown. The crest-to-crest distance is 8.0 cm, and the maximum displacement of all the masses is 1.5 cm. 1) Explain how you can tell that a...
  42. O

    Ramsey fringes - free oscillations

    i´ve got a question concerning Ramsey interferometry and fringes. Consindering the case we have 2 pi/2 pulses as usual. For this case it is easy to calculate the mean value of the Bloch component w by applying a rotation matrix, say rotating around the Bloch component v. Then applying a rotation...
  43. J

    Explaining Light intensity with EM Field Oscillations?

    I have understood that the frequency of an EM wave is caused by the frequency by which a charged particle oscillates, which causes its electrical field to periodically change its strength with respect to a fixed location point at a distance from that particle. The more energy (heat) you add to...
  44. yecko

    What is the amplitude of the resulting oscillations?

    Homework Statement A mass of 2.0 kg hangs from a spring with a force constant of 50 N/m. An oscillating force F = (4.8 N) cos[(3.0 rad/s)t] is applied to the mass. What is the amplitude of the resulting oscillations? Neglect damping. Answer: 0.15 m Homework Equations F=kx , the mass only...
  45. G

    Resonance in forced oscillations

    Homework Statement Consider the differential equation: mx'' + cx' + kx = F(t) Assume that F(t) = F_0 cos(ωt). Find the possible choices of m, c, k, F_0, ω so that resonance is possible. Homework EquationsThe Attempt at a Solution I know how to deal with such problem when there is no damping...
  46. G

    Finding the period of small vertical oscillations

    Homework Statement I need to find the period of small vertical oscillations about equilibrium position of a string whose motion can be described by the following equation: d2x/dt2 = (-g/h)*x Answer: 2π√(h/g) Homework Equations I know that the time period is given by the formula T = 2πω where...
  47. Hamal_Arietis

    Large oscillations of pendulum

    Homework Statement Find the large oscillation period T of pendulum. Suppose that the amplitude is ##\theta_0## We can write oscillation period T by the sum of a series, know that: $$\int_0^1 \frac{dt}{\sqrt{(1-t^2)(1-k^2t^2)}}=\frac{\pi}{2} \sum_{n=0}^{∞}(\frac{(2n)!}{2^{2n}(n!)^2})^2$$ Let...
  48. Hamal_Arietis

    I How to Solve Large Oscillations of a Pendulum?

    When I solve this problem i have the equation: $$x''+Asinx=0$$ How solve this equation if x large? I think we use some approximations
  49. M

    What causes oscillations in EM wave fields?

    I've been trying to understand what an electromagnetic wave is, and have spent quite a while now reading around and piecing different bits of information together to try and get an answer. I haven't yet found an answer to my title question. It might just be because I have a lack of...
  50. L

    Oscillations: mass in the center of an octahedron -- eigenvalues?

    You have an infinitesimally small mass in the center of octahedron. Mass is connected with 6 different springs (k_1, k_2, ... k_6) to corners of octahedron. Equilibrium position is in the center, you don't take into account gravity, only springs. Find normal modes and frequencies. Relevant...
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