I Which is Better for Measuring Vibrational Systems: Free or Forced Vibration?

[yecko]

Problem Statement: How to measure the natural frequency and damping ratio of a vibration system?
Why are the advantages over one another?
Relevant Equations: natural frequency, damping ratio of a vibration system

I think there are two ways: free & forced vibration.
forced is used because it is easy to be calibrated (?)
but why sometimes free vibration is used instead?
thanks

[Moderator's note: Moved from a homework forum and thus the template.]

 

[pointlessgomboc]

The main difference between free and forced vibrations is that a free vibration occurs without friction; whereas a forced vibration is when a repeated force occurs on a system, a periodic force would have to be applied for a forced vibration to be sustained. Therefore it can be seen that within a free vibration energy will remain the same, where no external force is applied on the system, and thus the results may be more accurate than that when measured with forced vibrations. Hopefully this is of some help to your question.

 

[BvU]

Problem Statement: How to measure the natural frequency and damping ratio of a vibration system?
Why are the advantages over one another?
Relevant Equations: natural frequency, damping ratio of a vibration system

I think there are two ways: free & forced vibration.
forced is used because it is easy to be calibrated (?)
but why sometimes free vibration is used instead?

Hi,
You want to study the harmonic oscillator (are probably doing that already, right? Very, very important in almost all areas of science and engineering).

The equation describing an unforced one is $${d^2x\over dt^2} +2\zeta\omega_0 {dx\over dt}+\omega_0^2 x=0$$with the righthand zero replaced by some acceleration in the case of forcing -- but even then the solution of the unforced case is relevant.

In many cases a step response is easier to implement and quicker to realize as investigation tool (think process technology, Laplace transform, cybernetics, ...). The mathematical analysis yields the desired parameters.

In other cases a frequency analysis (often with a sinusoidal driving force) can provide those values (and more detailed info); areas like mechanical engineering, electronics, ...

I am unhappy with the classification of @pointlessgomboc (i.e. I think it's wrong...). See the lemma.

[edit] Haha, the original post is four years old. So this reply is purely for the benefit of pointless...$\$

 

[vanhees71]

I would say the most accurate measurements are possible with applying harmonic forces with different frequencies and measure the amplitude and phase shift of the oscillator relative to these quantities of the applied force in the stationary state, i.e., after the transient part has been damped away. From these two quantities you can calculate $\omega_0$ and $\zeta$. The derivation of the formulae is a bit lengthy for a newsgroup posting. It can be found in many introductory mechanics textbooks.

 

[BvU]

Again, post #1 is four years old !

 

[pointlessgomboc]

Hi,
You want to study the harmonic oscillator (are probably doing that already, right? Very, very important in almost all areas of science and engineering).

The equation describing an unforced one is $${d^2x\over dt^2} +2\zeta\omega_0 {dx\over dt}+\omega_0^2 x=0$$with the righthand zero replaced by some acceleration in the case of forcing -- but even then the solution of the unforced case is relevant.

In many cases a step response is easier to implement and quicker to realize as investigation tool (think process technology, Laplace transform, cybernetics, ...). The mathematical analysis yields the desired parameters.

In other cases a frequency analysis (often with a sinusoidal driving force) can provide those values (and more detailed info); areas like mechanical engineering, electronics, ...

I am unhappy with the classification of @pointlessgomboc (i.e. I think it's wrong...). See the lemma.

[edit] Haha, the original post is four years old. So this reply is purely for the benefit of pointless...$\$

Hi, I think the question was why free vibrations are sometimes used instead of forced vibrations, not the graphed and calculated oscillations right? Technically, the advantages that led to free vibrations are used sometimes are because that they are a relatively closed system? Sorry I am not very sure of the question and your explanation...

 

[scottdave]

...
[edit] Haha, the original post is four years old. So this reply is purely for the benefit of pointless...

Several of these old unanswered posts have been revived. I think it has the benefit of if somebody comes upon PhysicsForums via a search engine.