ilovephysics.com :: free online physics help, tutorials, forums, classes, misconceptions in / Simple Harmonic Motion and Damping

SnackMan78 · 2006-04-04 00:12:15

Textbook Question:

Which one of the following terms is used to describe a system in which the degree of damping is just enough to stop the system from oscillating?

a) Slightly damped
b) Underdamped
c) Critically damped
d) Overdamped
e) Resonance

Textbook says that the smallest degree of damping that completely eliminates the oscillation is termed "critical damping". (This example has no picture to illustrate it.) Then a couple of lines later in the textbook, "Typical automobile shock absorbers are designed to produced underdamped motion somewhat like that in curve 3. (an illustration that highlights the best scenario of the motions: underdamped and undamped motion)

My answer is C based on the first textbook example, but I want to get confirmation from others. Any other thoughts?

Chris · 2006-04-04 00:54:23

Any amount of damping will cause the system to stop oscillating eventually. So the true answer would probably be "slightly damped" though that term seems to describe the same thing as "underdamped". I'm guessing your book would say "slightly" is a case of "under" to a small degree.

But what your textbook is groping at is "Critically Damped". This is the point when the damping completely eliminates the oscillation as soon as the damping force is applied.

The frequency of oscillation of a damped oscillator, $\omega '$ , is given by:

$\omega ' = \omega_{0}\sqrt{1 - \frac{b^2}{4km}}$

$\omega_{0}$ = undamped frequency
b = damping coefficient (how much damping)
k = spring constant
m = mass.

The oscillator is underdamped if $\omega'$ is real, which will be true if $4km > b^2$ . It will undergo true oscillations, eventually approaching zero amplitude due to damping.

The oscillator is critically dampled if $\omega'$ is zero, when $4km = b^2$ . The oscillator will not oscillate - it will go to zero exponentially in the shortest possible time.

The oscillator is overdamped if $\omega'$ is imaginary, which will be true if $4km < b^2$ . The amplitude goes to zero exponentially as before, but over a longer time and does not oscillate through zero at all.

Announcement

#1 2006-04-04 00:12:15

Simple Harmonic Motion and Damping

#2 2006-04-04 00:54:23

Re: Simple Harmonic Motion and Damping

Board footer