What is Oscillations: Definition and 517 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

    LC Oscillations seem impossible to me

    Current increases up to a certain point, and then decreases until it reaches zero. Then it does the same thing in the other direction. Here's my problem. Without the inductor, the current would not increase over time: it would decay until the two plates had equal charge. With the inductor, I...
  2. L

    (Small oscillations) Finding Normal modes procedure.

    Homework Statement The first part of the problem is just finding the Lagrangian for a system with 2 d.o.f. and using small angle approximations to get the Lagrangian in canonical/quadratic form, not a problem. I am given numerical values for mass, spring constants, etc. and am told to find the...
  3. A

    How Is Kinetic Energy Related to Spring Compression in Harmonic Motion?

    A 4 kg mass is attached to a 100 N/m spring and oscillates with an amplitude of 0.75 m across a horizontal frictionless surface. When the kinetic energy is 70% of the total mechanical energy, by how much is the spring stretched or compressed? I'm not sure how to approach this problem. I could...
  4. N

    Central Force (period of revolution and period of small radial oscillations)

    [b]1. A particle of mass m and angular moment L moves in a central force V=(1/2)kr^2 (k>0). Find the period of revolution for the circular movement and the period of small radial oscillations around the stable cicular orbit. Homework Equations The Attempt at a Solution Well I tried...
  5. S

    Physics-Stable Equilibrium and Oscillations

    Homework Statement A one-dimensional force F(x)=(3.0N/sqrt(m))*sqrt(x)-(1.0N/m)x acts on an object of mass m = 2.57kg. a Find the position x0 where the mass is at a stable equilibrium. b Find the frequency of small oscillations around that equilibrium position. How does this compare to...
  6. K

    Oscillations of a Pendulum: How Many Complete by Noon and What is the Amplitude?

    Homework Statement In a science museum, a brass pendulum bob swings at the end of a 15m long wire. The pendulum is started at exactly 8:00 a.m. every morning by pulling it 1.5m to the side and releasing it. Because of its compact shape and smooth surface, the pendulum's damping constant is...
  7. S

    How Long Does It Take for a Mass to Oscillate Between Two Points on a Spring?

    Homework Statement A vertical spring stretches 9.6 cm when a 1.3kg block is hung from its end.This block is then displaced an additional 5.0 cm downward and released from rest. Calculate the time it takes the object to go from a point 0.025 m below its equilibrium position to a point 0.025 m...
  8. W

    Forced oscillations and ressonance

    Hi friends, I will be right to the point. On the book "Mechanics" by Landau & Lifgarbagez, chapter "Small Oscillations", section "Forced Oscillations": 1. What is the meaning of the term beta (phase constant) on the expression for the driven force, F(t) = f cos(gamma t + beta), how it...
  9. T

    Solving Oscillations in an Electrical Circuit

    Homework Statement a. What is the frequency of the current oscillation of the circuit as it is shown? b. What is the frequency of the oscillations in electrical potential difference, V, between the two ends of the resistor in the circuit as it is shown? c. What is the charge on the...
  10. A

    Oscillations of a complicated spring block system

    Homework Statement A 4kg block M in horizontal plane is attached to a sprig S1 fixed to a light rod OA of length 4m as shown in diagram(refer to attachement). The other end O of the rod is hinged to rotate in the plane about the vertical axis passing through it. A spring S2 is fixed to the mid...
  11. J

    Electrical oscillations of an RLC circuit

    Electrical oscillations are initiated in a series circuit containing a capacitance C, inductance L, and resistance R. a) If R << \sqrt{\frac{4L}{C}} what time interval elapses before the amplitude of the current oscillation falls to 50.0% of its initial value? b)Over what time interval does...
  12. Z

    Force Oscillations: Approximating Amplitude & Energy Decreases

    Homework Statement A lightly-damped oscillator is set in motion and observed as the oscillations decrease in amplitude. Derive approximate values for the factors by which i) the amplitude, and ii) the energy will decrease after Q cycles, where Q is the “quality parameter” defined in the...
  13. L

    How Is Maximum Acceleration Calculated in a Harmonic Oscillator?

    I need help with this question. The potential energy stored in a harmonic oscillator at time t0 = -0.5 s is 1 mJ. The spring-constant associated with the oscillator has the value k = 103 N m-1 and the oscillation amplitude is A = 10-6 m. Calculate the magnitude of the maximum acceleration.
  14. S

    LC oscillations with DC source

    Homework Statement Suppose we have a circuit with the inductor, uncharged capacitor, ideal battery with emf E all in series. At t=0, the circuit is switched on. The following takes place sequentially: 1. Current at t=0 is max. Battery charges capacitor, current decreases. 2. inductor...
  15. N

    Oscillations, velocity, elasticity

    Homework Statement A 0.2 kg object, suspended from a spring with a spring constant of k = 10 N/m, is moving in simple harmonic motion and has an amplitude of 0.08 m. What is its velocity at the instant when its displacement is 0.04 m? Homework Equations v=root(F/m/l) The Attempt...
  16. JJBladester

    Damped oscillations in a vacuum chamber

    Homework Statement A 200 g oscillator in a vacuum chamber has a frequency of 2.0 Hz. When air is admitted, the oscillation decreases to 60% of its initial amplitude in 50 s. How many oscillations will have been completed when the amplitude is 30% of its initial value? Homework...
  17. P

    Oscillations between planets, gravitational work

    Homework Statement Centers of masses of planets mass m1 i m2 and radius r1 i r2 are standing still on a distance l. What is the distance between point T (which is located on a place where graviation is 0) and the surface of the first planet? How much work do we do if we move a body of...
  18. A

    Free oscillations of a metre rule

    Homework Statement Hi Everyone. I came across this problem: A metre rule is clamped to a table so that part of its length projects at right angles from the edge of the table. A 100g mass is attached to the free end of the rule. When the free end of rule is depressed downwards then released...
  19. F

    Damped Oscillations. Mass Hanging from a spring

    Damping is negligible for a 0.121 kg mass hanging from a light 6.55 N/m spring. The system is driven by a force oscillating with an amplitude of 1.45 N. At what frequency will the force make the mass vibrate with an amplitude of 0.465 m? There are two possible solutions, enter one of them...
  20. P

    How to Approach Oscillations Homework Problems

    Homework Statement I attached a file containing the problem statement, because it is impossible to reproduce all the symbols. Homework Equations Also in the attached file. The Attempt at a Solution I tried to simply substitute theta but it turned out to be very messy...
  21. R

    Small oscillations around equilibrium point in polynomial potential

    Hi guys i am a bit confused about this problem, a particle of mass, m, moves in potential a potential u(x)=k(x4 - 7 x2 -4x) I need to find the frequency of small oscillations about the equilibrium point. I have worked out that x=2 corresponds to the equilibrium point as - dU/dx = F =...
  22. S

    Bungee Jumping: Solving for Mass, Cord Length, and Period of Oscillations

    Homework Statement A bungee jumper leaps from a bridge and undergoes a series of oscillations. Assume g=9.78 m/s^2. If a 58.0 kg bungee jumpers jumps from length of 20.0 m and she jumps from a heigh of 66.0 m above the river, coming to rest a few centimeters above the water surface on the...
  23. I

    How Does Archimedes' Principle Affect Damping in Harmonic Oscillations?

    Hi, I'm trying to build up a mass spring system, which is damp by a small steelball lowered into a buck containing soap mixture. Where the viscosity has been measured and we have calculated the flow arround the ball to be rather laminar (Reynold<1). But our data shows a damping around the double...
  24. S

    Oscillations of an elliptic PZT tube

    Hi I am trying to solve for the energy potential inside the cavity of an oscillating cylinder. At first, I solved the wave equation for an axisymmetric cylindrical cavity. Since the cavity is a perfect cylinder , the boundary condition was a constant at the surface of the cylinder (as...
  25. N

    Water oscillations in a U-tube

    Homework Statement Consider a column of liquid (density ρ) of length ℓ confined in a U-tube of uniform cross-sectional area A. Suppose that the water level on one side is pushed down a small amount and then released. 1) Construct expressions for the potential and kinetic energies of the...
  26. J

    Finding Equation of Motion for Oscillations Using Lagrangian Methods

    1. A rigid straight uniform bar of mass m and length l is attached by a frictionless hinge at one end to a fixed wall so that it can move in a vertical plane. At a distance a from the hinge it is supported by a spring of stiffness constant k, as shown in the figure Ignoring gravitational...
  27. J

    Mass on a tensioned cable with axial/transverse oscillations

    Homework Statement This problem isn't actually assigned homework for me, but I wanted to see if I get the concept. Any feedback and corrections to my answer would be appreciated! A cable is stretched between two anchors, and a small mass is attached to the cable, through the center of the...
  28. C

    Period of oscillations of the disk

    Homework Statement A circular disk of radius R and uniform density is free to pivot about a fixed point P on its circumference. Calculate the period of oscillations of the disk, in the plane of Figure I, when it is displaced by a small angle about its pivot and released. Homework...
  29. K

    How do I calculate the maximum height of a pendulum swing?

    Homework Statement A pendulum consists of a 1.5kg mass swinging at the end of a string of length 2.0m. At the lowest point in the swing the tension in the string is equal to 20N. To what maximum height above this lowest point will the mass rise during its oscillation? Homework Equations...
  30. H

    Forced Oscillations (proving diff equation by subsitution)

    Homework Statement By substituting the proper equations I showed that the equation is right when time = phi/w. Now when I make cos = o and sin = 1 and time = (pi/2 - phi)/w I can't solve the equation. Homework Equations If you need to see all the equations i can give it to you but I am...
  31. S

    Oscillation Frequency of superposition of two oscillations of different frequencies

    Homework Statement Find the frequency of combined motion of the following (a) x = sin (12pi.t) + cos(13pi.t + pi/4) (b) x = sin(3t) - cos(pi.t) Homework Equations The book I'm using states that if the periods are commensurable ie if there exist 2 integers n1 and n2 such that n1T1 =...
  32. V

    Forced oscillations vs Natural frequency

    What happens if the frequency of the forced oscillation is Pi / 2 radians out of phase of the natural frequency of the spring mass system? I guess this makes the amplitude of the spring mass system to oscillate at a maximum amplitude.. Am I correct? Thanks in advanced..
  33. M

    Exploring Oscillations: Investigating the Relationship Between T, m_eff, and k

    Homework Statement In the lab, we had a hanging spring. We proceeded to add mass to the spring (starting at 100g, and increasing by 50g until 500g) and timed the period of oscillation, T, for each mass added. We also found the spring constant by finding the slope of Displacement vs. Mass...
  34. R

    Are there enough information to solve these oscillation and wave problems?

    Ok first time poster here so I hope I do this right. 2 assignment q's out of four I got I'm having trouble with. I think there might be missing info but I'm hoping for someone to back me up on this or to point me in the right direction. Homework Statement Q.1 Consider two identical ideal...
  35. T

    Average Energy - Oscillations

    Homework Statement Express the ratio of the average kinetic energy K to the average total energy E of the oscillator in terms of the dimensionless quantity ωo/ω. Homework Equations I found that: K = (1/2)mA^2ω^2 sin^2(ωt − δ) E = (1/2)mA^2[ω^2 sin^2(ωt − δ) + ωo^2 cos^2(ωt − δ)] The...
  36. K

    Mass difference corresponding to atmospheric oscillations

    Hi, In arXiv:hep-ph/0307149v2, it is mentioned that atmospheric mass-squared difference is not uniquely defined and that the convention that is going to be used is that it is the largest possible mass-squared difference. I know that the smallest mass difference is identified with solar...
  37. P

    Periodic oscillations in the output signal

    Dear All, We have an voltage amplifier. The input is given in small square wave steps to check rise time and noise level of an output signal. The rise time looks good, but we see periodic (noise)oscillations after reaching the plateau. We measure signal voltage across capacitor (10 micro...
  38. TrickyDicky

    What exactly are Baryon acoustic oscillations?

    What exactly are Baryon acoustic oscillations? How do we detect them? How are they used to build a "ruler" of cosmological parameters? How are BAOs related to the late time ISW effect? and to dark energy? Lots of questions, hopefully someone here can give me some answers or at least some...
  39. S

    Quick Clarification Question (Oscillations)

    Homework Statement Homework Equations The Attempt at a Solution I just have a quick question about http://answers.yahoo.com/question/index?qid=20081217223328AAQd6nj&r=w&show_comments=true&pa=FZB6NWHjDG3N56z6v_2wWb4ed4wHUvdybUFUU_dDvWAH.7iY1ZZYRg--&paid=add_comment#openions" When the...
  40. S

    Oscillations: Damped Block homework

    Homework Statement The drawing to the left shows a mass m= 1.9 kg hanging from a spring with spring constant k = 6 N/m. The mass is also attached to a paddle which is emersed in a tank of water with a total depth of 34 cm. When the mass oscillates, the paddle acts as a damping force given by...
  41. E

    Oscillations - A puzzling demonstration

    I watched MIT OCW PHYSICS 8.01 lectures, and in lecture no.13, i saw a puzzling demonstration. Link :http://ocw.mit.edu/OcwWeb/Physics/8-01Physics-IFall1999/VideoLectures/detail/embed13.htm" I don't understand, what can be the reason for the oscillations of ball on the track with the...
  42. B

    Oscillations of a ruler on a cylinder

    Homework Statement You have ruler of length L and thickness 2d resting, in equilibrium , on a cylindrical body of radius r. Slightly unbalancing the ruler, and existing attrition between the surfaces prove that the ruler has a oscillatory motion of period: T = 2\cdot \pi\cdot...
  43. A

    Understanding Forced Damped Oscillations at Resonance and Low Frequencies

    Homework Statement At the natural frequency,ω0 what are the real and imaginary components of Avel(ω) ? Sketch a phasor diagram with the velocity vector and driving force vector,and use this to provide the phase difference between Avel(ω) and the driving force if ω=ω0 (ι.e at resonance)...
  44. A

    Damped Forced Harmonic Oscillations

    Homework Statement If F0= 0 and γ<<2ω0 where γ=b/m, sketch the resulting wave-form for displacement with time.Define Q,the quality parameter,and show on your sketch how the value of Q, influences the waveform Homework Equations mψ'' =-kψ-bψ' +F0exp(-iωt) The Attempt at a Solution...
  45. F

    How Do Rocking Bowl Oscillations Relate to Torque and Moment of Inertia?

    Homework Statement A hemispherical shell with its curved surface resting on a table will rock back and forth. To derive the period, use \sumT=I\alpha_{}z. Sum the torques about the instantaneous point of contact and make the small angle approximation sin \theta\approx\theta. You will need...
  46. M

    Spring Constant and Oscillations -

    Homework Statement A 1.450 kg air-track glider is attached to each end of the track by two coil springs. It takes a horizontal force of 0.700 N to displace the glider to a new equilibrium position, x= 0.290 m. a.) Find the effective spring constant of the system. b.) The glider is...
  47. I

    Walking legs as physical pendulum oscillations

    Homework Statement The typical walking speed of a person walking at a relaxed pace can be estimated by modelling their legs as a physical pendulum. Assume that the length of a person's leg is L and it pivots about the hip and the leg is tapered (more mass towards the hip and less towards the...
  48. B

    Oscillations Spring constant Newton's second law

    So i have the equation m*(d2x/dt^2)+c*(dx/dt)+kx=0, where d2x/dt^2 is the second derivative. So I'm given that m=10 kg, and k=28 N/m. At time t=0 the mass is displaced to x=.18m and then released from rest. I need to derive an expression for the displacement x and the velocity v of the...
  49. A

    What is the amplitude of the subsequent oscillations?

    A 375 g air-track glider attached to a spring with spring constant 9.50 N/m is sitting at rest on a frictionless air track. A 425 g glider is pushed toward it from the far end of the track at a speed of 96.0 cm/s . It collides with and sticks to the 375 g glider.a)What is the amplitude of the...
  50. P

    Significance of L/E in neutrino oscillations

    Dear fellow Physicists, I am writing to ask what the significance of the term (L/E) in neutrino oscillation is? From my initial understanding it determines the oscillation mode, so if you have an experiment of a baseline of 300km, you can adjust the neutrino beam energy to suit the particular...
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