Forced oscillations Definition and 31 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. Z

    Force transmitted to a block in viscous fluid through a spring, cord, and pulley

    The equation of motions looks like $$m\ddot{x}(t)+m\Gamma\dot{x}(t)=-K(x(t)-d_0\cos{\omega_d t})\tag{3}$$ Moving other end of the spring sinusoidally effectively produces a sinusoidally varying force on the mass. Everything written above so far is as presented by the book "The Physics of...
  2. P

    I Infinite value of amplìtude of an undamped driven oscillator at resonance

    So if we set the damping constant ##\beta=0## that is if we consider an undamped oscillator the amplitude becomes infinity! What is the physical meaning of this phenomena? As we know energy fed into the system is proportional to ##A^2##. So does this mean that an infinite amount of energy is...
  3. Y

    Functional representation of the oscillating graph

    Hi; This is in fact not a homework question, but it rather comes out of personal curiosity. If you look at the graph of the two functions in the image attached, what is the simplest functional representation for such a symmetrical pattern?
  4. Tymofei

    Influence of initial shift on undamped frictionless forced oscillations

    I have general equation for undamped forced oscillations (no friction) which is: I just wonder about,what type of motion should occur when initial conditions are both 0 (i.e v0=0 and x0=0). My intuitive expectation is that as there is no 'natural' oscillations at beginning,vibration has to be...
  5. 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...
  6. E

    B Determining ansatz for forced oscillations in SHM

    I've generally solved introductory second order differential equations the 'normal' way; that is, using the auxiliary equation, and if it is inhomogeneous looking at the complementary function as well, and so on. I know that sometimes it can be helpful to propose an ansatz and substitute it...
  7. Alettix

    Exponential Forcing Differential Equation

    Homework Statement Solve ## \frac{d^2y}{dt^2} + \omega^2y = 2te^{-t}## and find the amplitude of the resulting oscillation when ##t \rightarrow \infty ## given ##y=dy/dt=0## at ##t=0##. Homework EquationsThe Attempt at a Solution I have found the homogenious solution to be: ##y_h = A\cos\omega...
  8. 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...
  9. G

    Forced oscillations and resonance (bis)

    I'm studying from landau lifšits "mechanics". I had some troubles in section small oscillations-->forced oscillations, especially from eq 22.4 to eq 22.5 i searched the web and came across this: https://www.physicsforums.com/threads/forced-oscillations-and-ressonance.488538/#post-3236442 this...
  10. J

    Forced oscillations: solution of Differential Equation at resonance

    Homework Statement Following a worked example in my book, I have been trying to get a solution for the equation \frac{d^2u}{dt^2} + \frac{k}{m}u = Fcos\omega t The book says that at resonance, i.e. when \omega_0 (the natural frequency) = \omega (the forcing frequency), the term F cos\omega...
  11. applestrudle

    Forces in Damped Forced Oscillations?

    The example I'm thinking of is a mass spring system. x = Ae^(\gamma/2)t cos(wt +a) + Ccos(wt) If the steady state has been reached, the displacement due to the free oscillations will be negligible, so does that mean that the only force acting on the mass is the driving force, F0cos(wt)...
  12. J

    Forced Oscillations - Why Amplitude Reaches Fixed Value at Zero Frequency?

    Hi, why is it that as the frequency of the driver decreases below the natural frequency of the oscillator it reaches a fixed amplitude when the external frequency is zero whereas whenever you go to the other extreme and have a very high external frequency the amplitude of the oscillator...
  13. D

    Forced oscillations in a discrete system

    Hello Everyone! Homework Statement There exists a very large (discrete) system of N coupled masses, each of mass "m", where every pair is connected via a spring of constant "K". Assuming all motion is horizontal, find the amplitude of the oscillations of an nth mass in the system, under the...
  14. D

    Forced oscillations without damping

    Homework Statement We are to develop the equations of motion for an undamped horizontal spring system, the mass of which is being driven by a periodic force: F=F0 cos wt. I know how to do it but my teacher has defined an odd term, the meaning of which I want to be clarified. Homework...
  15. R

    How do you find the force extended if given the amplitude? Forced Oscillations

    How do you find the force extended if given the amplitude? Is main questions, I also have one slight question. Ok, doing a problem. There is no damping. A (.15kg) object is hanging from a light(6.30N/m) spring. A sinusoidal force with an amp of 1.7 N drives the system. And the problem is...
  16. T

    The frequency of forced oscillations

    So the frequency of an oscillator is always the same as the frequency of the force, if that force is a sinusoidal function of time. What's the best way to visualize why this is so? And also, why is the frequency of the oscillator in phase with the force if the force is below the resonance...
  17. E

    Steady state behavior for a particle undergoing damped forced oscillations

    Homework Statement consider a system with a damping force undergoing forced oscillations at an angular frequency ω a) what is the instantaneous kinetic energy of the system? b) what is the instantaneous potential energy of the system? c) what is the ratio of the average kinetic energy to the...
  18. D

    Forced Oscillations: +ve Sign of Fcoswt

    In the equation of forced oscillations (given below), ma = -kx + FCoswt, why is that the 2nd term on the right hand side is given the +ve sign. I know that kx should be negative since 'ma' and 'x' are in opposite directions. I can't quite seem to get the gist of Fcoswt being given a +ve...
  19. 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...
  20. 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...
  21. 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..
  22. W

    Forced oscillations of a linear system

    Hello, I am currently working on a lab in which we are studying the behaviour of chain of metal bars attached together with nylon wire in such a way as to to mimic the ability of solids or liquids to transmit a wave. After studying the normal modes of the system as well as the quality...
  23. J

    How Do You Solve Pure Resonance in Undamped Forced Oscillations?

    Homework Statement This is an example of an Undamped Forced Oscillation where the phenomenon of Pure Resonance Occurs. Find the solution of the initial value problem: x'' + 4 x = 8 sin(2 t) , x(0)=x'(0)=0 Homework Equations The Attempt at a Solution in class we were given...
  24. J

    Finding Displacements for forced oscillations

    Homework Statement A particle of mass m is at rest at the end of a spring (force constant = k) hanging from a fixed support. At t = 0 , a constant downward force F is applied to the mass and acts for a time t_0 . Show that, after the force is removed, the displacement of the mass from...
  25. N

    Forced Oscillations of Mass-Spring System: Reasons for Observed Behaviour

    A mass spring system with natural frequency of 1.5Hz is set up as shown: http://img300.imageshack.us/img300/7922/35809066dx2.th.jpg Can someone please explain the reasons for the following observations: When the support rod oscillates at a frequency of 0.2 Hz - oscillations are...
  26. H

    Forced Oscillations Homework: Determine Period & Amplitude

    Homework Statement A 2.00 kg object attached to a spring moves without friction and is driven by an external force F=(3.00N) sin(2pie t). Assuming that the force constant of the spring is 20.0 N/m determine (a) the period and (b) the amplitude of the motion. Homework Equations T = 2pi...
  27. K

    Solve Damping & Forced Oscillations Problems: Frequency, Amplitude & More

    I was hoping someone could explain damping and forced oscillations. I had a couple of problems I could not do that revolved around these topics because I couldn't figure out which equations to use. Here's an example. 1. Homework Statement Damping is negligible for a 0.155 kg object...
  28. G

    Trigonometric identity forced oscillations

    Homework Statement http://www.jyu.fi/kastdk/olympiads/2004/Theoretical%20Question%203.pdf http://www.jyu.fi/kastdk/olympiads/2004/Solution%203.pdf Question A- (b) They use some trigomentric identity that I don't understand, which one is it? Thanks in advance. Homework...
  29. A

    How Many People Cause a Bridge to Oscillate with a 75 mm Amplitude?

    I'm doing this problem from Mastering Physics, and I'm really stuck on this problem Assume that, when we walk, in addition to a fluctuating vertical force, we exert a periodic lateral force of amplitude 25 N at a frequency of about 1 Hz. Given that the mass of the bridge is about 2000 kg...
  30. N

    Forced Oscillations: Period & Amplitude Calculation

    A 2.00 kg mass attached to a spring is driven by an external force F = (2.00 N) cos (3t). Assume that the force constant of the spring is 25.0 N/m. (a) Determine the period of the motion (b) Determine the amplitude of the motion FOr part A, i tried the T=2(pi)/w formula, and i got...
  31. S

    Forced Oscillations: Does the Solution Reduce to Oscillations When F_0=0?

    For forced oscillations we have \frac {d^2x} {dt^2} = -\omega_N^2x+\frac {F_0} {m} cos\omega_Ft The solution is x(t)=\frac {F_0} {m(\omega_N^2-\omega_F^2)}cos\omega_Ft This doesn't seem to reduce to oscillations where F0=0. Shouldn't it?
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