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Topic: Simple Harmonic Motion (SHM)
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Subject:   Simple Harmonic Motion (SHM)
Author: Sione
Date: Feb 5 2004
Craig,

Ok, believe I misread your response was to Steve rather than to my post.

I am not a teacher, so I cannot debate on what not and what is taught in class
room at what level. I can only bring issues relating to my understanding of
mathematics .

>It is possible for simple harmonic motion to result in >values not symmetric
around zero--it just depends on >initial conditions.

Yes , it does. I never said that it cannot. I pointed out that SHM is always
symmetric from equilibrium.  
May be I need to clarify some taxonomy here.

Oscillations --> Harmonic Motions(HM) --> Simple Harmonic Motions (SHM).


Oscillations is the general class of motions. It means motion that repeats
itself. Harmonic Motions (HM) is a type of Oscillations. The frequency or period
of HM is constant , that is fixed for ALL time. Simple Harmonic Motion (SHM) is
a type of HM where the the equilibrium is at position ZERO (or time ZERO if it
is a function of time). YEP , that is the definition of SHM which is Equilibrium
at ZERO. I believe you confused the conditions for HM and SHM. SHM must always
and have constant frequency (which implies that the period and and wavelength is
also fixed at all time). Physical examples are water waves, sound waves,
pendulum, spring-mass, simple electronic filters (low-pass, band-pass,
high-pass) also known as tuning circuits with applications such as tuning to a
particular radio station, etc, etc. For a general HM, the requirement for an
equilibrium at ZERO is relaxed, then you can have situation as you described as
non-symmetric motion. Physical examples are electronic pump amplifies where a
constant power source is added into an oscillating one (an AC source), which
result in relations like the following:

    Y = Yo*Sin(w*t + phi) + A

The amplitude of the above equation is non-symmetric.

Another type of HM is non-linear. The conditions that frequency is fixed is
also relaxed. Frequency is allowed to vary or change over time in non-linear
HM. This means that you can have waves that the wavelength shrinks or expand
over time. Physical example is a type of pulse that called CHIRP. It is used in
medical instrumentation for ultra-sound in clinical applications. The
ultra-sound emitted short pulses of high frequency waves. Initially when the
device is turned on, it starts at an initial frequency and it changes (fast
sweep) to the higher ranges in a short period of time. This process is repeated
over and over until you turn off the the ultra-sound device. If the sound
waves were SHM (fixed frequency, and symmetric amplitude) , the device will not
get a good picture or reflection from body tissues. The reasoning for sweeping
the frequency in a range and not fixed, is because body tissues have different
densities therefore reflect sound waves differently, so a good signal is
captured by the ultra-sound device when you have  back-scattered waves also
in different frequencies.

I should stop there because it is too long.

Finally, is SHM is taught in Maths at high school level in the US? In here in
New Zealand , the topic is not taught in Maths but it is in senior high school
Physics. I am surprised when I see posting to MathForum about the SHM topic and
I immediately assumed it is part of the Maths curriculum for high school in the
US.

Till Next Time,
Cheers,
Sione.


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