Part 1
HARMONIC OSCILLATIONS
Oscillatory motion is everywhere in nature.
Any object which has both inertia and a restoring force
will oscillate around an equilibrium position if displaced from that equilibrium. As we will see, the
descriptions of essentially all oscillating systems are very similar  and hence we will look most closely
at massspring systems and pendula, the most common oscillators in our daily experience.
Describing the motions of objects that oscillate about a point of equilibrium, as with the motion of
any object, requires a solid understanding of Newton's laws. It is useful at this point to review the
essential ideas contained in those laws. As we will then see, the descriptions of the motions of masses
on springs, pendula, marbles oscillating about in the bottom of a bowl, and even the periodic motions of
buildings or bridges or violin strings will follow from understanding the forces acting and then solving
Newton's second law.
So we will begin with a review of Newton's laws of motion.
NEWTON'S LAWS
While the kinematics equations describe the motions of objects, it is Newton's three laws that relate
the motion to the
causes
of the motion.
As simple as Newton's laws are at one level, it is difficult to
overemphasize their importance.
They represent the fundamental principles that govern how things
move  the connection between how objects interact with each other and the changes in motion that result
from that interaction.
Solving Newton's law problems is often very difficult for many students. To be
successful at it requires
internalizing
what is actually meant by Newton's laws  not just learning the
statements or knowing the equation that expresses Newton's second law.
When Newton's laws are
understood, setting up problems to solve for the motion of some object simply becomes an exercise in
identifying all the forces on the object and expressing Newton's second law in algebraic form
speciallized to each object in the specific problem being described.
Newton's 1st Law:
The Law of Inertia
In the absence of a net force  or unbalanced force, an object either remains at rest
or moves in a straight line at constant speed.
The first law just identifies that
changes
of motion occur because of forces  and so the state of
motion remains unchanged either if no forces act or if all the forces that do act are balanced in such a
way to add to zero.
This is the basis of all equilibrium problems.
The
inertia
of an object is its tendency to remain in its current state of motion. The object's mass is
a measure of its inertia.
The significance of the first law is to state that because of the inertia of an
object, an unbalanced force is required to change the object's motion.
Newton's 2nd Law:
The Law of Motion
The result of a net force (or unbalanced forces) on an object is an acceleration in
the direction of the net force.
The acceleration will be directly proportional to
the net force and inversely proportional to the mass of the object.
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 Winter '08
 Sharpe
 Force, Inertia, Pendula Newton

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