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. Runei

    Solution: Solving Harmonic Oscillation Differential Equation

    Hello, When I have the differential equation \frac{dY(x)}{dx} = -k^2 Y(x) The solution is of course harmonic oscillation, however, looking at various places I see the solution given as: Y(x) = A cos(kx) + B sin(kx) instead of Y(x) = A cos(kx + \phi_1) + B sin(kx + \phi_2) Isnt...
  2. 6c 6f 76 65

    Harmonic oscillation; new amplitude?

    Homework Statement A block with a mass M is located on a frictionless, horizontal surface and is attached to a horizontal spring with spring stiffness k. The block is being pulled out to the right a distance x=x_0 of equilibrium and released at t = 0. At time t_1, corresponding to \omega...
  3. X

    Oscillation in spring mass system questions

    Homework Statement I am having an issue with answering number 4 in the attached image. Homework Equations Relevant equations are given in question 3. The Attempt at a Solution Squaring the equation would only make it easier to solve for any of the other variables, or the period...
  4. Saitama

    Oscillation of a solid hemisphere

    Homework Statement I don't have the exact wordings of the problem statement. I hope the following is enough to understand the problem. A solid hemisphere is kept on a plane horizontal frictionless surface. The hemisphere is made to tumble (or toss, I am not sure about the correct word)...
  5. X

    Finding the Right Answer: Tips for Solving Oscillation Problems

    I apologize ahead of time for all of these post about oscillation. I am trying to learn this stuff on my own. I answered "a" because the x^2 function. But I don't know the second part.. Would it also be 3x^2 because it is proportional to the x(t) function?
  6. X

    Simple Harmonic Motion: Question about w(t+T)=wt+2pi

    I have a quick question about simple harmonic motion. My text states this in the picture attached, and I'm confused as to why: w(t+T) = wt+2pi wT=2pi I assumed w would distribute out into the first expression. I know this may be a dumb question but please help because it is bothering me...
  7. O

    Solve for Period of Oscillation of 2 Springs with Mass Attached

    Homework Statement You have two springs with spring constants k_1 = 10 and k_2 = 20 vertically attached to a wall, and a mass of mass 3.00kg is hung from it. Find the period of oscillation. ---------------- || || <-- first spring, k_1 = 10 || -- || || <== second...
  8. C

    How Do You Determine Normal Modes in a Coupled Spring System?

    Homework Statement So I'm given two horizontal masses coupled by two springs; on the left there is a wall, then a spring with k_{1}, then a mass, then a spring with k_{2}, and finally another mass, not attached to anything on the right. The masses are equal and move to the right with x_{1}...
  9. J

    What is the resulting period of the oscillation?

    Homework Statement A 0.16-kg mass is hanging from a spring with spring constant 14 N/m. Then the mass is displaced from the equilibrium by 2.9 cm and let go. Homework Equations the period is the time for a one full cycle so the equation would be T= 2∏sqrtm/k The Attempt at a...
  10. J

    What is the resulting frequency of the oscillation?

    Homework Statement A 0.31-kg mass is hanging from a spring with spring constant 13 N/m. Then the mass is displaced from the equilibrium by 3.3 cm and let go. Homework Equations for frequencthy the equation would be 1/T The Attempt at a Solution to T I would use this equation...
  11. J

    What is the resulting angular frequency of the oscillation?

    Homework Statement A 0.65-kg mass is hanging from a spring with spring constant 15 N/m. Then the mass is displaced from the equilibrium by 2 cm and let go. Homework Equations angular frequency:ω=2∏/T The Attempt at a Solution I found T: 2∏sqrtm/k, 2∏sqrt0.02/15N/m= 0.229429488s...
  12. I

    How is the steady periodic oscillation used to solve problems?

    I have a homework problem that I need to use the steady periodic oscillation to solve, so instead of having help on the problem I'd rather just understand how they did it then apply it to my homework (I think that's alright?) I'm kind of wondering where my book gets this from...
  13. amjad-sh

    Electomagnetic oscillation in lc circuit

    Hi, We know that when we connect a charged capacitor to a coil, the capacitor will discharge in the coil that means that the current will flow in the circuit in decreasing manner with respect to time .So an emf will be created in a way that oppose the decrease. Bin will has the same...
  14. C

    Period of Oscillation for vertical spring

    Homework Statement A mass m=.25 kg is suspended from an ideal Hooke's law spring which has a spring constant k=10 N/m. If the mass moves up and down in the Earth's gravitational field near Earth's surface find period of oscillation. Homework Equations T=1/f period equals one over...
  15. S

    Oscillation of a Bose Einstein condensate in an harmonic trap

    Homework Statement We were asked to try to make a theoretical description of the following phenomenon: Imagine a 2D Bose Einstein condensate in equilibrium in an harmonical trap with frequency ω. Suddenly the trap is shifted over a distance a along the x-axis. The condensate is no longer...
  16. U

    Small oscillation equation derivation

    Hi guys, I have been trying to find the "floppy" resonant mode frequency of a simple oscillator. The displacement is in the order of nanometers, while the dimensions of the oscillator is in cm. I think small angle approximations apply here. I got to the point of the equation of motion, but I...
  17. Saitama

    Time period of oscillation and gravitation

    Homework Statement Homework Equations The Attempt at a Solution I really don't know how to start with this problem. The four point masses of mass m oscillate together so I am confused as to how should I begin making the equations. Just a guess, should I write down the expression for potential...
  18. B

    Saw-tooth Wave and Fourier Series amplitude of oscillation

    Homework Statement An oscillator with free period \tau is critically damped and subjected to a force with the saw-tooth form \F(t)=c(t-n\tau) for (n-0.5)\tau<t<(n+0.5)\tau for each integer n. Find the amplitudes a_n of oscillation at the angular frequencies 2\pi n/\tau if c is a...
  19. G

    What is anharmonicity and how does it relate to oscillation?

    For my physics lab report, we are supposed to conduct an experiment to show the non-harmonic oscillation of a simple pendulum. I know what is simple harmonic oscillation, damped oscillation, driven damped oscillation. But what is a non-harmonic oscillation? A google search reveals that there...
  20. R

    Why do neutrinos always have a specific flavor when detected?

    Hi, this is probably pretty simple but it's puzzling me... In neutrino oscillation, you produce and detect neutrinos with a specific flavour (e,μ,τ) but they travel as mass eigenstates (1,2,3). The flavour eigenstates are just linear superpositions of mass eigenstates: nu_e = U_e1 nu_1 +...
  21. M

    Differential equations of forced oscillation and resonance

    How do I derive A? As you can see in the attachment, I tried to substitute x and expand the equation but I got stuck. How do I get rid of the δ and cos and sin to get the result in the end? Please help!
  22. S

    Problem of Oscillation of mass attached to spring with external force

    Homework Statement A particle of mass m is attached to a spring (of spring constant k) and has a natural angular frequency ω0. An external force. F(t) proportional to cos ωt(ω ≠ ω0) is applied to the oscillator. The time displacement of the oscillator will be? Homework Equations F=-kx...
  23. Avi Nandi

    Time period of oscillation of a physical pendulum and spinning disk

    Homework Statement Find the period of a pendulum consisting of a disk of mass M and radius R fixed to the end of the rod of length l and mass m. How does the period change if the disk is mounted to the rod by a friction less bearing so that it is perfectly free to spin? The centre of the...
  24. S

    Longitudinal plasmon oscillation

    Kittel solid state physics book ( chapter 14)says when dielectric permittivity is zero, then longitudinal polarization wave possibly exists. It is hard to imagine how this is possible. Can anybody explain this? If the permittivity is zero, then there shouldn'n be any response, right? How come...
  25. Saitama

    Calculating time period of oscillation

    Homework Statement Homework Equations The Attempt at a Solution (see attachment 3) If the middle charge is moved a y distance, then the other two move a distance y/2 in opposite direction. Similarly, the velocity in y direction of other two can be also calculated. As the rods are rigid, the...
  26. G

    Simple Harmonic Oscillation Problem

    Homework Statement The velocity of an object in simple harmonic motion is given by v(t)= -(4.04m/s)sin(21.0t + 1.00π), where t is in seconds. What is the first time after t=0.00 s at which the velocity is -0.149m/s? Homework Equations N/A The Attempt at a Solution I thought this was...
  27. F

    Synchronized coupled harmonic oscillation

    Given a general solution to the fixed-end two-mass coupled harmonic oscillator(http://teacher.pas.rochester.edu/PHY235/LectureNotes/Chapter12/Chapter12.pdf), is there a set of initial conditions for position, velocity, the 3 spring constants, and 2 masses such that a transition from random phase...
  28. M

    Second order differential equation.(Damped oscillation)

    Hi could do with a little help with this question please! The question A damped oscillation with no external forces can be modeled by the equation: \frac{d^2x}{dt^2}+2\frac{dx}{dt}+2x=0 Where x mm is amplitude of the oscillation at time seconds. The initial amplitude of the...
  29. O

    What is the underdamped frequency of an oscillation?

    A mass is attached to a spring in underdamped oscillation, the damped frequency is ω^2=( ω1 )^2 -(∂/2m)^2 where ω is the damped angular frequency ω1 is the natural angular frequency ∂ frictional coefficient m is the mass attached to the spring is the damped angular frequency is constant...
  30. A

    Einstein notion of time and the oscillation of the cesium atom

    I just read the thread entitled: "How did Einstein Define Time" and I'm very confused. At school, I was taught that time was an abstract representation of movement meaning that the word "time" can only be used to represent movements. For example, when Earth has completed a cycle around the...
  31. S

    Solving for Oscillation with Given Parameters

    Homework Statement Solve: ##\ddot{x}+\Omega^{2} x=D+\frac{C}{2}+Ecos\omega t+\frac{C}{2}cos2\omega t## Homework Equations The Attempt at a Solution I got a hint to use ##x=\alpha sin\omega t+\beta cos\omega t## so ##\ddot{x}=-\alpha ^{2}\omega ^{2}sin\omega t-\beta ^{2}\omega...
  32. R

    Using displacement, velocity and acceleration oscillation equation?

    Homework Statement The function x = (4.5 m) cos[(6∏ rad/s)t + ∏/3 rad] gives the simple harmonic motion of a body. At t = 1.6 s, what are the (a) displacement, (b) velocity, (c) acceleration, and (d) phase of the motion? Also, what are the (e) frequency (in Hz) and (f) period of the...
  33. S

    When does a Particle Come to Rest and Reach Maximum Velocity During Oscillation?

    Homework Statement A particle oscillates about a fixed point. Its distance, x(m) from the origin is given by the equation x=3sin(2t) + 2cos(2t) -2. Find i) its velocity, ii) where it first comes to rest, iii) its maximum velocity.Homework EquationsThe Attempt at a Solution Well firstly...
  34. Physics Monkey

    Stable oscillation of a blanket in a dryer?

    Hi everyone, Today I noticed something curious while I was drying a blanket in a dryer. The dryer was turning and the blanket was jumbling around as usual, but then I realized the motion was approximately periodic. This periodic motion was strange to me. Of course, the dryer is driven on a...
  35. T

    Angular Oscillation of a rod in a circle

    Homework Statement A uniform rod moves in a vertical circle .Its ends are constrained to move on the track without friction.Find the angular frequency of small oscillation .Homework Equations The Attempt at a Solution Suppose the rod of length L moves in a circle of radius R . Let the...
  36. M

    Linear Algebra: Solving a system of equations for damped oscillation

    So we are given two equations: $$ \ddot{x} - \dot{x} - x = cost (t) $$ and $$ x(t) = a sin(t) + b cos(t) $$ The question asks to find a and b. How would one go about doing this? I thought maybe substituting the $$ cos(t) $$ from equation 1 into equation 2 would work but then what...
  37. E

    Wave interference and harmonic oscillation

    1. when wave is destructive interference ,where is the energy? for example, two plane wave have opposite phase ,they will destructive interference completely,but where is the energy? in antireflection film, the reflection wave is disappear!why? where is the energy? where is the wave? 2.in what...
  38. C

    Concept Problem: Oscillation and friction

    So I feel as though I have the correct solution, but am not positive. My problem is as follows: A block of mass M is at rest with respect to a surface which oscillates horizontally with sinusoidal motion described by the equation x(t)=Asin(ωt). Find an expression for the minimum value of the...
  39. E

    Estimating damping factor for steel in flexural oscillation

    I am trying to estimate the damping ratio of steel in bending. I have a situation where I need to know the dynamic response of an inverted pendulum. A picture is worth a thousand words, so here you go: The vibration will be free; it is caused be the initial position of the system. I can...
  40. H

    How to derive the equations of oscillation

    I am new to this site. I have a problem with the derivations of second order equations for SHM. F= -kx F+kx+0;ma+kx=0 m(second time derivative of x)+k(first time derivative of x)=0 As my textbook says above equation implies that x(t)=Acos(ωt+∅) But I can't understand why. From where did...
  41. H

    Trying to understand the oscillation of electrons in the magnetic fiel

    Working on understanding the physics of how an electron oscillates along the Earth's magnetic field. I understand that an electron will spiral around the magnetic field line, that's easy to tell from the Lorentz force. What I don't understand is what causes the oscillation. My best guess is...
  42. M

    Archived Oscillation with Green's Function

    Homework Statement A force Fext(t) = F0[ 1−e(−αt) ] acts, for time t > 0, on an oscillator which is at rest at x=0 at time 0. The mass is m; the spring constant is k; and the damping force is −b x′. The parameters satisfy these relations: b = m q , k = 4 m q2 where q is a constant...
  43. N

    Oscillation Frequency: Horizontal vs Inclined Plane

    How does the oscillation frequency compare when being horizontal and when being on an inclined plane (assuming frictionless). I thought this: When on Horizontal surface frequency = angular frequency (w) / 2∏ Since frequency does not depend on acceleration, the frequency would remain...
  44. C

    Oscillation of a vertical spring

    Homework Statement A mass m hangs in equilibrium at the lower end of a vertical spring of natural length a, extending the spring to be a length b. 1) Show that the frequency for small oscillations about the point of equilibrium is ##\omega = \sqrt{g/(b-a)}## 2) The top end of the...
  45. O

    Optimizing Physical Pendulum Oscillation: Finding d for Shortest Period

    Homework Statement A physical pendulum is created from a uniform disk of radius 12.0 cm. A very small hole (which does not affect the uniformity of the disk) is drilled a distance d from the center of the disk, and the disk is allowed to oscillate about a nail through this hole. If...
  46. A

    Why Does Boundedness of a Function Affect Its Oscillation?

    Suppose that f is bounded by M. Prove that ω(f^2,[a,b])≤2Mω(f,[a,b]). I can show that ω(f,[a,b])≤2M and that ω(f^2,[a,b])≤M^2 but this procedure is getting me nowhere. I also have a similar problem that likely calls for the same approach: Suppose that f is bounded below by m and that m is a...
  47. L

    Oscillation / Soundwaves Question - Phase difference?

    An observer stands 3 m from speaker A and 4 m from speaker B. Both speakers, oscillating in phase, produce 170 Hz waves. The speed of sound in air is 340 m/s. What is the phase difference (in radians) between the waves from A and B at the observer’s location, point P? And I have no idea how...
  48. P

    Electric field of ring causing oscillation

    Homework Statement A ring of radius 18 cm that lies in the yz plane carries positive charge of 5 µC uniformly distributed over its length. A particle of mass m that carries a charge of −5 µC executes small oscillations about the center of the ring on its axis with an angular frequency of...
  49. S

    Is this the correct approach? (finding frequency of oscillation)

    Homework Statement Find the frequency of small oscillations around the minimum of the potential U(x)=1-e^(-x^2) Homework Equations Force is the negative of the gradient of the potential... The Attempt at a Solution Given the problem statement bit, "around the minimum," I take this...
  50. N

    Harmonic oscillation with friction

    Hello, I want to include kinetic friction into the harmonic oscillator. A small blocks is attached to a horiontal spring on a table. Because there is kinetic friction there are two forces on the blok that we need to describe the oscillation. First, the force that the spring exerts and second...
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