http://www.ck12.org Chapter 10. Periodic Motion
10.1 Simple Harmonic Motion
Objectives
The student will:
- Understand periodic motion.
- Understand simple harmonic motion.
Vocabulary
- periodic motion:Motion that repeats the same path at a regular time.
- simple harmonic motion:A kind of one-dimensional (back-and-forth) periodic motion in which the farther
the object moves from the center, the more it is pulled back toward the center.
Introduction
The word periodic simply means something that repeats at regular intervals, such as days of the week (weekly),
birthdays, and holidays (yearly). Periodic motionis motion that repeats the same path –round-and-round, back-
and-forth, or similar. Familiar cases of periodic motion include the Earth orbiting the Sun (Figure10.1) and an
elastic collision of a ball rebounding off of a flat surface (Figure10.2). Two very important vibrating motions
discussed in this chapter are objects vibrating on the end of springs and pendulums.
A special case of periodic motion issimple harmonic motion (SHM). This is a particular kind of back-and-forth
motion, in which the farther the object moves from the center, the more it is pulled back. Two common cases of
SHM are:
- A pendulum on a string (called a simple pendulum). The farther out the pendulum swings, the more gravity
pulls it back. - A mass vibrating on a spring. The more the string is stretched or squashed, the more force it exerts.
SHM is especially important because it serves as a model for related processes. Similar vibrations of molecules are
responsible for sound, and similar vibrations of electrically-charged particles at a microscopic scale are responsible
for radio waves, light, and x-rays.
Simple Harmonic Motion from Uniform Circular Motion
An object vibrating back and forth on the end of a spring is an example of simple harmonic motion (SHM). For
such motion, the force responsible for the vibration is directly proportional to the object’s displacement. Other
examples of objects performing SHM are the tuning fork inFigureabove, a lightly plucked taut string, some forms
of molecular vibrations, and pendulum motion close to the bottom of its swing. It is by no means obvious but as we
shall see, SHM is related to uniform circular motion.