Re: vibration vs. oscillation

["Carl E. Mungan" <mungan@USNA.EDU>]

Hi Debora: I haven't seen much of you this summer. I basically agree
with what you wrote, but add a few additional thoughts:

> 1. A particle has no extend.

I would rather say a particle has no accessible internal degrees of
freedom. Its size is irrelevant.

> Its position is described by a single coordinate.

Yes, and it often makes sense to take that to be the coordinate of
its center of mass (COM). See Chabay and Sherwood's textbook for lots
of interesting discussion of what they call the "point-particle
system".

> A real object may be considered a particle if all points on the particle
> undergo the same displacement in the same delta-t.

Very clear. An inertial coordinate system is of course implied.

> 2. A particle cannot rotate or vibrate; it can only translate.

Yes, this follows from your previous sentence. I would add that
rotational and vibrational energies are therefore forms of internal
energy--they are relative to the COM--in contrast to the bulk
translational energy.

> 3. A particle can oscillate. For example, a particle can be attached to a
> spring which provides a restoring force and causes the particle to oscillate.
> (The spring is not part of the particle)

Yes, or a simple pendulum bob say.

> 4. A system may consists of many particles. If the particles are oscillating,
> then the system is said to vibrate. Such examples include a plucked violin
> string, a stuck bell or a running motor.

I follow the examples of the violin string and struck bell. I note
these are interesting examples in which we begin with nonthermal
internal energy that gradually becomes thermalized over time.

I am not so sure about the motor. I think I would rather call that
rotational than vibrational. On the other hand, I am not sure the
distinction really matters too much, as a torsional pendulum could be
called either one, I suppose.

OTOH, it seems to me that vibratory systems involve stretching -
displacement of one particle relative to adjacent particles. This
doesn't happen for a spinning disk. Perhaps the torsional pendulum
really consists of 2 subsystems: a rotating disk plus a twisting
spring, where a twist is a special kind of vibrational mode. Carl
--
Carl E. Mungan, Asst. Prof. of Physics  410-293-6680 (O) -3729 (F)
      U.S. Naval Academy, Stop 9C, Annapolis, MD 21402-5040
mailto:mungan@usna.edu       http://usna.edu/Users/physics/mungan/