influences on people's lives--a belief that is reflected even today in horoscopes
and astrological publications. A revolution in man's thinking that occurred
about four hundred years ago established the concept of a solar system with
planets orbiting about the sun and moons orbiting about some of the planets.
Copernicus, Kepler, Galileo, and Newton were the four scientific leaders chiefly
responsible for establishing this new viewpoint. One of its very practical aspects,
yet difficult for us earth-bound creatures to grasp, is that the force of gravity
gradually diminishes as one recedes from the earth, in a way beautifully stated by
Newton in his universal law of gravitation.Gravity is a universal force: it acts
on every material thing from the smallest nuclear particle to the largest galaxy. It
even acts on objects that have zero rest mass, such as photons--the fantastically
minute "chunks" in which light comes. One of the most exciting areas of
astronomical research today is the "black hole," where the gravitational field
may be so immense that not even light can escape!Newton's law of gravitation
is important not only in itself, but also because it serves as a model for the
interaction of electric charges, which you will study later. Not only are the force
laws and the potential-energy functions nearly the same, but the concept of a
field carries over and becomes even more useful in the calculation of forces
between electrically charged particles.
PREREQUISITE: Relating the resultant force acting on a particle to the particle's
mass and acceleration.

Week of March 16, 1998
Lesson 10Simple Harmonic Motion
Keywords: waves, simple harmonic motion, oscillations; : Calculus; Period;
Amplitude; Frequency; Fundamental Motion; Properties Of Waves; Simple
Harmonic Motion; Newton's Second Law; Differential Equations
OBJECTIVES:
* Write Newton's second law for a particle undergoing simple harmonic motion in
one dimension and write the general solution for the resulting differential
equation.
* Define the following terms as they relate to a simple harmonic oscillator:simple
harmonic motion,amplitude,frequency (herz),phase constant (or phase
angle),angular frequency,period, spring constant,restoring force.
Given the necessary information about a system oscillating harmonically in one
dimension, solve for any of the following: position as a function of time, angular
frequency, period, amplitude, frequency, velocity, acceleration, mass, restoring
force.
Comments: Have you ever felt you were the slave of a clock? Clocks are
mechanisms that include a pendulum or balance wheel whose repeated patterns of
movement define equal time intervals, one after another. Such repeated
movements are called periodic motion. Periodic motion may occur when a particle
or body is confined to a limited region of space by the forces acting on it and does not
have sufficient energy to escape.In this lesson you will study the special kind of
periodic motion that results when the net force acting on a particle, often called the
restoring force, is directly proportional to the particle's displacement from its