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. A

    Forced Oscillation; general question.

    I've got a fairly basic question of mathematical strategy, what technique is used to solve the problem of a forced periodical (but not sinusoidal) oscillation with damping? Do I simply find the general solution to the differential equations of motion?
  2. V

    Total energy oscillation problem

    Homework Statement The displacement of a mass m = 0.01 kg is x(t) = 0.25m sin(62.83t/s − 0.785398) Find its amplitude, its total energy, and its speed at t = 0. Homework Equations E = Av^2 + Bx^2 x = Asin(wt-theta) The Attempt at a Solution i use that above formula to...
  3. M

    Period of Oscillation in a 1D Linear Spring

    Homework Statement The question I have a one-dimensional linear spring with spring constant E. The tension is given by σ = Eε, epsilon = strain.. The left side of the spring is held fixed, the right side has a mass m attached to it. We can neglect gravity. What is the natural oscillation...
  4. P

    Period of oscillation for a mass on a spring

    Why does the period of oscillation for a mass on a spring depend on its mass? (while in other situations, like a simple pendulum, the mass seems to be unimportant)
  5. B

    Oscillation of a spring and mass on an asteroid

    Homework Statement Find the period of oscillation T of the spring and mass on the asteroidHomework Equations T=2\pi\sqrt{\frac{m}{k}}The Attempt at a Solution I have found the value for T but was wondering if T depends on the bodies gravity? Is the above equation only applicable to Earth?
  6. M

    Natural oscillation period for elastic spring

    Homework Statement I have a linear elastic spring with spring constant E, The spring is mass less, and is held fixed at the left terminal and has a mass m attached on the right terminal. We can neglict gravitational forces. Find the natural oscillation when the tension sigma = E*epsilon...
  7. M

    Mechanical Oscillation and Resonance

    Homework Statement A mechanical oscillator system is driven sinusoidally with a force amplitude, F(max). The Oscillator resonates at 27Hz. When driven with the same F(max) at 26Hz or 28Hz, the resulting oscillation has half the amplitude as at resonance. When F(max) is instead applied...
  8. 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 =...
  9. W

    Damped Oscillation: Finding Time Constant

    Homework Statement The amplitude of an oscillator decreases to 36.8% of its initial value in 10.0 s. What is the value of the time constant? Homework Equations xmax=Ae^-bt/2m Time constant= m/b xmax(t)= Ae^-t/2(timeconstant) The Attempt at a Solution I'm not quite sure where to...
  10. L

    Vertical oscillation frequency

    Homework Statement Let’s assume the MilkyWay disk in the Solar neighborhood has a constant density,P = 0.15 M pc−3. In that case, what is the vertical oscillation frequency in the Solar neighborhood? What is the oscillation period? Homework Equations p=2pie/v from my mechanics class i...
  11. S

    Finding Time in an Oscillation Problem

    Homework Statement Here on Earth you hang a mass from a vertical spring and start it oscillating with amplitude 2.4 cm. You observe that it takes 3.0 s to make one round trip. You construct another vertical oscillator with a mass 6 times as heavy and a spring 3 times as stiff. You take it to...
  12. K

    General calculation of the oscillation freq of a hydrogen molecule

    Homework Statement Okay here's the problem, normally I can get all this stuff, but right now this is blowing my mind, partly because its too general. "In other problems and examples in the textbook we found the effective spring stiffness corresponding to the interatomic force for aluminum...
  13. J

    Solving a Parabolic Bowl Oscillation Problem

    Homework Statement Consider a particle moving back and forth on a frictionless parabolic bowl, y = ax2, where a = 1.460 m-1 If the particle is released from rest at the point on the bowl at b = 0.43 m, find the period of the oscillations. I have an equation for velocity(as a function of...
  14. J

    Find the steady-state oscillation of the mass–spring system modeled by the given ODE.

    Homework Statement Find the steady-state oscillation of the mass–spring system modeled by the given ODE. Show the details of your calculations. Homework Equations 1. y'' + 6y' + 8y = 130 cos 3t 2. 4y’’ + 8y’ + 13y = 8 sin 1.5t The Attempt at a Solution 1. cos(3t) at the end means the...
  15. A

    Damped Oscillation problem.

    Homework Statement Help need with this problem. A light spring AB of natural length 2a and of modulus of elasticity 2amn2 lies straight at its length and at rest on a smooth horizontal table. The end A is fixed to the table and a particle P of mass m is attached to the midpoint of the spring...
  16. neduet

    What is the purpose of reactive power in motors?

    Hi friends ""Active power is the share of the apparent power which transmits energy from the source (generator) to the user. Reactive power is the share of the apparent power which represents a useless oscillation of energy from the source to the user and back again"" This Texts from a...
  17. A

    What Is the Frequency of Oscillation in a Series RLC Circuit?

    Homework Statement A resistance of 100 ohm is connected in series with capacitor 0.1 microF and an inductance 10 mH. find the frequency of oscillation and value of current at resonance? Homework Equations f= 1 / 2*pi*sqrt(LC) The Attempt at a Solution i think the formula i use for...
  18. A

    Calculating Spring Constant for Mechanical Oscillation

    A 4.0kg block extends a spring 16cm from its unstretched position.The block is removed and a 0.50Kg body is hung from the same spring.If the spring is stretched and released,the period of oscillation is : a)0.28s b)0.02s c)0.42s My Work : T = 2pi/w T = 2pi*sqrt{Mass Totall/K} I...
  19. S

    Torsion Pendulum Oscillation (SHM)

    Homework Statement A uniform meter stick is hung at its center from a thin wire. It is twisted and oscillates with a period of 5 s. The meter stick is then sawed off to a length of 0.76 m, rebalanced at its center, and set into oscillation. With what period does it now oscillate...
  20. L

    Mastering Physics: 'weighing lunch': spring oscillation

    Homework Statement For lunch you and your friends decide to stop at the nearest deli and have a sandwich made fresh for you with 0.100 {\rm kg}of turkey. The slices of turkey are weighed on a plate of mass 0.400 {\rm kg} placed atop a vertical spring of negligible mass and force constant of...
  21. D

    Looking for formula to equate force to oscillation frequency/length

    Hi, i am interested in figuring out the tension strength on a guitar string, by using its oscillation frequency (or fundamental harmonic) and its length.. I looked online but can't find much... I tried some dimensional analysis but couldn't come up with much
  22. W

    What is the arc length of a pendulum bob with mass m and length l?

    a pendulum bob of mass m hangs on a string of length l. what is the espression for the arc length of the bob if its discplaced through an angle theta.
  23. B

    Solving the Oscillation of Mass-Spring System

    Homework Statement Mass m attached to spring with spring constant k=Am. It feels a resistive force magnitude Bmv where v is the speed. and A, B are constants such that 4A > B^2 What is the fractional change in amplitude of oscillation in one complete oscillation? Homework Equations...
  24. S

    Damoed Oscillation in an RLC circuit

    Homework Statement A single loop circuit consists of a 7.2 ohm resistor, a 12.0 H inductor, and a 3.20*10^-6 F capacitor. Initially the Capacitor has a charge of 6.20*10^-6 C and the current is zero. Find the charge on the capacitor N complete cycles later for a) N=5, b) N=10, and c) N=100...
  25. S

    Opposing spring oscillation with mass

    Homework Statement A 36 kg mass is placed on a horizontal frictionless surface and then connected to walls by two springs with spring constants k1 = 3 N/m and k2 = 4 N/m. What is the frequency, f (in Hz), of oscillation for the 36 kg mass if it is displaced slightly to one side...
  26. S

    Pendulum and spring oscillation

    Homework Statement A 5 kg sphere is connected to a thin massless, but rigid rod of length L = 1.3 m to form a simple pendulum. The rod is connected to a nearby vertical wall by a spring with spring constant k = 75 N/m, connected to it at a distance h = 1.1 m below its point of...
  27. S

    Finding angular frequency of damped oscillation

    My question is that I am asked to find the angular frequency of a spring-mass system. I am given the damping constant, the mass of the object at the end of the spring, the mass of the spring, and the spring constant. I know that angular frequency equals the square root of the spring constant...
  28. E

    Finding Oscillation Amplitude?

    Homework Statement I have a problem where I am given the following values: Angular Oscillation Frequency which I have assigned to omega Spring Constant, which is k The system's kinetic energy in Joules. Phi is assumed to be 0 I am asked to find the oscillation amplitude at a certain...
  29. M

    Calculating Oscillatory Motion Parameters for a Spring-Block System

    Homework Statement A 0.7 kg block attached to a spring of force constant 13.4 N/m oscillates with an ampli- tude of 20 cm. Find the maximum speed of the block. Answer in units of m/s. (part 2 of 4) 10.0 points Find the speed of the block when it is 10 cm from the equilibrium position...
  30. G

    Speed of oscillation of free electrons

    Homework Statement Find maximum speed of oscillation of a free electron near Earth’s surface due to Sun’s electromagnetic field. Find out the ratio of maximum magnetic force acting on the electron Fm to the maximum electric force Fe. Regard Sun’s radiation as monochromatic with wavelength...
  31. D

    Oscillation conditions: Feedback phase shift

    One of the conditions for oscillation is that the (regenerative) feedback loop must provide a 180 degree phase shift. This is due to the fact that, for a regenerative effect, the signal must undergo n*360 degrees phase shift: 180 from the amplifier and another 180 from the feedback network...
  32. K

    Work and Power of the Friction Force in an F=-bυ damped oscillation

    Hey there forum! Consider a damped oscillation in which the friction force is F=-bυ. What I want to ask is how do you calculate the work done by this force for any x interval along a line and what is the Power of the work done by this force? I already know that Power P of the work done...
  33. X

    Ring oscillation formula derivation

    Homework Statement Derive and show that the period for a thick ring would be T=2π√[d/g+(ΔR)^2/4Rg] Homework Equations I'm not sure... The Attempt at a Solution Obviously, delta R means the difference between Ri and Ro would be considerable. So ΔR=Ro-Ri. Then Ro=R+ΔR/2 and...
  34. S

    Solving a Model Car Oscillation Question: Find Vmax & Velocity

    We have been given this as a sample exam question. For a car store a small model car (75kg) is hung from the ceiling. The model is hanging on an elastic spring with force constant 1500 N/m. The model is oscillating 10 times per second with an amplitude of 0.02 m. (Assume a zero-phase shift)...
  35. J

    Simple Harmonic Oscillation: Solving for Period, Frequency, Energy, and Velocity

    Homework Statement A block of mass 5 kg is attached to a spring of 2000N/m and compressed a distance of 0.6m. The spring is then released and oscillates. a. what are the period, frequency, and angular frequency b. what is the energy in this system c. what is the maximum velocity...
  36. P

    Coupled oscillation: time interval between maxima

    Homework Statement I calculated T_o to be 1.27 seconds and "T_o"' to be 1.23 seconds, each representing a normal mode of oscillation. These are correct according to the text. Here is the question: what is the time interval between successive maximum possible amplitudes of one pendulum after...
  37. L

    Electric Potential with oscillation

    Homework Statement A proton moves along the x-axis, where an arrangement of source charges has created the electric potential V=6000x^2, where V is in volts and x is in meters. (a) Graph the potential between x = -5.0 and x = +5.0. (c) By exploiting the analogy with the potential energy of a...
  38. M

    Period of Oscillation of Steel Ball

    I already did the first part, and the equation for the period becomes: T=2\pi(ml/\gammaPA)(1/2) I know 12 litres = 0.012 m3, and the the mass of the ball is the volume of a sphere of radius 0.01m x the density = 0.0318 Kg, for pressure I am not sure whether I am suppose to use 1 atm or 101.3...
  39. T

    How is the formula for period of oscillation derived?

    How is the formula for period of oscillation derived? t=2pisqrt(m/k)
  40. 1

    Finding how weight placed on a ruler affects its oscillation.

    Homework Statement I'm currently having a bit of trouble figuring out how to most effectively execute my experiment. It's somewhat practical; I need to find how the masses placed on the end of a vibrating ruler will affect its oscillation. I know that the ruler is a standard 12 inch (30.5...
  41. N

    Oscillation frequency of probability density P(x,t)

    If an electron is in an infinite 1-D square well of width L, how do you get oscillation frequency of the probability density for any energy state n?
  42. O

    Particle in Stable/Unstable Motion, Find Frequency of Oscillation

    Homework Statement A particle moves around the surface of an upside-down cone, in a horizontal circular path, in equilibrium. The particle is given a small radial kick. Use the Lagrangian equation for motion (found in a previous section of this problem): m\ddot{r} =...
  43. U

    Oscillation / Phase Space Question

    Homework Statement Thornton and Marion, chapter 3, problem 21: Use a computer to produces a phase space diagram similar to Figure 3-11 for the case of critical damping. Show analytically that the equation of the line that the phase paths approach asymptotically is \dot{x}=-\beta x. Show...
  44. P

    Solve Oscillation Problem: |v|=0.5v_max

    Homework Statement A block attached to a spring is displaced from equilibrium to the position x = +4.9 m and released. The period is 0.5 s . At what positions and times during the first complete cycle do the following condition occur: | v | = 0.5 v_{max}, Where v_{max} is the maximum speed...
  45. V

    Designing a Fluid-Powered Oscillation Mechanism for Rotating Water Outlet Lines

    I would like to rotate a water outlet line 180 degrees using the water pressure as the force driving the rotation. Does anyone know of any designs for an application like this? Perhaps some type of a butterfly valve under tension to one side? As the pressure builds behind the closed...
  46. L

    Another amplitude and oscillation problem

    Homework Statement A small earthquake starts a lamppost vibrating back and forth. The amplitude of the vibration of the top of the lamppost is 6.5 cm at the moment the quake stops, and 8.0 seconds later it is 1.8 cm. A. What is the time constant for the damping of the oscillation? _____...
  47. L

    Oscillation, Frequency, Amplitude etc Hmwk Problem

    Homework Statement A 200g mass attached to a horrizontal spring oscillates at a frequency of 2.0 Hz. At one instant, the mass is at x=5.0cm and has vx = -30cm/s. A. Determine the period. T= ____seconds B. Determine the amplitude. A =____cm C. Determine the maximum speed. vmax =...
  48. D

    Solve Neutrino Oscillation Unit Conversion Problem

    Homework Statement I doubt that my problem is supposed to be in the Advanced Physics forum, but the subject is advanced. Okay, my problem is pretty stupid. The assignment is deriving a probability using some approximations and such, for 2-neutrino oscillation. I can do the entire calculation...
  49. A

    What's quality factor in oscillation ?

    What's "quality factor" in oscillation ? I want to know why and how it was defined ? Is it useful in some ways ?
  50. W

    Oscillation Period in a Lighthouse?

    Homework Statement A visitor to a lighthouse wishes to determine the height of the tower. She ties a spool of thread to a small rock to make a simple pendulum, which she hangs down the center of a spiral staircase of the tower. The period of oscillation is 10.4 s. The acceleration of gravity...
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