Does the frequency of an object in vacuum remain constant

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Your vibrating system has a certain natural frequency of oscillation. For example for a simple pendulum that is $\sqrt \frac gl$ where $l$ is the length of the pendulum and for a spring mass system the frequency is $\sqrt \frac km$ where $m$ is the mass and $k$ is the spring constant.
You will note that these natural frequencies $f_N$ are characteristic of the systems not of something outside the system.

Now call your system the driveN system and apply an external force to your system calling it the driveR with a frequency $f_R$ and amplitude $A_R$.

Initially the motion of your driveN system will be complex being composed of oscillations at the natural frequency of your system $f_N$ and at the frequency of the driveR $f_R$.

The oscillations at the natural frequency will eventually die away and are called transient for that reason. What you will be left with are so called steady state forced oscillations of your system at the frequency of the driveR $f_R$.
In general the amplitude of the driveN system will not equal the amplitude of the driveR but if the amplitude of the driveR is increased so proportionately will the amplitude of the driveN system increase.

Now you say that you do not believe your book that the frequency of your driveN system will not be the same as the external driveR.
Well just get hold of the suspension point of a simple pendulum and move it backwards and forwards very very slowly.
You are the driveR and the pendulum is the driveN oscillating at the same frequency as the movements of your hand.
If you move the point is suspension very slowly the pendulum bob will follow you hand.
The complication with this demonstration is that unless you move the point of suspension very slowly you will excite the bob to also oscillate at its natural frequency and that transient motion for your driveN system will take a long time to die away.

The other important thing about the steady state behaviour of your driveN system is that if the amplitude of the driveR stays constant but the frequency of the driveR is changed the amplitude of the driveN system changes.
At a particular frequency of the driveR the amplitude of the driveN system becomes a maximum and that contain is called resonance.
For small amounts of damping resonance occurs when the frequency of the driveR $f_R$ is equal to the natural frequency of the driveN system $f_N$.


So for your driveN system undergoing steady state forced oscillations

  • at a constant driveR frequency the amplitude of the driveN system is proportional to the amplitude of the driveR
  • at constant driveR amplitude the amplitude of the driveN system depends on the frequency of the driveR and the driveN system has a maximum amplitude (resonance) when the frequency of the driveR is approximately equal to the natural frequency of the driveN system
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Updated on December 05, 2022

Comments

  • MrAP
    MrAP 19 days

    Suppose there is an object(say a pendulum) in vacuum. When a force of certain magnitude is applied on this object, it starts vibrating with a particular frequency and amplitude. Now if the magnitude is increased (or decreased) will the frequency and amplitude with which the object vibrates change or will it remain constant?

    This topic is dealt with in my book under the topic "Natural/ Free vibrations". My book says they will not change. The natural frequency is a characteristic property of an object. I do not believe my book since i find it impossible and non-intuitive to imagine this.

    • Admin
      Admin almost 6 years
      What book? What does it have to do with vacuum? But yes, frequency of a harmonic oscillator is independent of amplitude. A pendulum is a reasonable approximations as long as the amplitude is not too large.
    • MrAP
      MrAP almost 6 years
      @Pieter, it specified vacuum because, if a medium is present, damping occurs.
    • Admin
      Admin almost 6 years
      Even in vacuum there would be damping (the suspension, the wire).
    • MrAP
      MrAP almost 6 years
      What do you mean by a harmonic oscillator? We have not been taught this.
    • Admin
      Admin almost 6 years
      Galileo Galilei was bored in church, started timing the swinging chandeliers with his pulse, and found out that the frequency remained the same, also when the amplitude had become much smaller. Observational fact. You do not need a vacuum to verify this.
    • MrAP
      MrAP almost 6 years
      I do not see how this answers my question. I had asked whether or not the frequency and amplitude of an object depend on the force applied and if they do then why?
    • Admin
      Admin almost 6 years
  • Admin
    Admin almost 6 years
    What waves? What do you mean by "size of waves"? What does this answer?
  • MrAP
    MrAP almost 6 years
    My question was about the vibrations of an object in vacuum where there is no external force acting on the object. A object is disturbed from it's mean position(force applied) and my book says that the object will continue vibrating forever with same frequency and same amplitude and the frequency is a characteristic of the body and does not change. This is where I am having problem. My question was why does the frequency and amplitude remain constant even on applying a different force. You have discussed in your answer "vibrations in a medium" more specifically forced vibrations.
  • Farcher
    Farcher almost 6 years
    Your disturbance i.e. pushing the system from the equilibrium position is really an external force (impulse) acting on the system. In such a case you are just observing the natural frequency oscillation of the system (the transient behaviour). The steady state behaviour is the pendulum at rest as there is no longer an external force. One of the characteristics of shm is that it is not amplitude dependent so where ever you start the motion of your system it will undergo oscillations at it natural frequency with the amplitude being dictated by the initial displacement that you gave the system.
  • MrAP
    MrAP almost 6 years
    Why does it's frequency remain constant?
  • Farcher
    Farcher almost 6 years
    If you look at the beginning of my answer you will see that the natural frequency of a system only depends on what the system is composed of length, mass, spring constant etc and not on external factors.
  • MrAP
    MrAP almost 6 years
    Why is that so?It is hard to imagine that the frequency is constant.
  • Farcher
    Farcher almost 6 years
    One of the characteristics of simple harmonic motion is that the frequency of oscillation does not depend on the amplitude of the motion. When you play a note on a musical instrument changing the loudness of a note does not change its frequency.
  • MrAP
    MrAP almost 6 years
    Ok. So in conclusion, in natural vibrations of an object, the frequency always has a constant value which is the natural frequency of the object, a characteristic property of the object and does not change on changing the external force while the amplitude may change. Right?
  • JMLCarter
    JMLCarter almost 6 years
    I mean oscilations of the body. Sorry about that - crossed wires. Like a string of a particular length and tension will emit a particular frequency of sound. This is the resonant frequency of the string.
  • Admin
    Admin almost 6 years
    I had suggested that @MrAP observe a pendulum, take the time of free oscillation, for a small amplitude and a larger amplitude. I don't think he has done that yet.
  • MrAP
    MrAP almost 6 years
    @Pieter Can i do that using an online pendulum simulator?
  • Farcher
    Farcher almost 6 years
    @MrAP I think that phet.colorado.edu/en/simulation/pendulum-lab will show the variation of period with amplitude of swing.
  • Admin
    Admin almost 6 years
    I do not understand why @MrAP and other students are so reluctant to conduct a simple real experiment: get some thread from your mother, tie some thing, let it swing.