Next: Elastic Potential Energy
Up: Vibrations and Waves
Previous: Vibrations and Waves
Idea: Any object that is initially displaced slightly from
a stable
equilibrium point will oscillate about its equilibrium position.
It will, in general, experience a restoring force that depends
linearly on the
displacement x from equilibrium:
Hooke's Law:
where the equilibrium position is chosen to have x coordinate
x = 0 and k is a constant that depends on the system under
consideration. The units of k are:

[k] = .
 (2)

Definitions:

Amplitude ( A ): The maximum distance that an object moves
from its equilibrium position. A simple harmonic oscillator moves
back and forth between the two positions of maximum displacement,
at x = A and x =  A .

Period ( T ): The time that it takes for an oscillator to
execute one complete cycle of its motion. If it starts at t = 0 at
x = A , then it gets back to x = A after one full period at t = T .

Frequency ( f ): The number of cycles (or oscillations) the
object
completes per unit time.

f = .
 (3)

The unit of frequency is usually taken to be 1 Hz = 1 cycle per second.
 Simple Harmonic
Oscillator: Any object that oscillates about a stable equilibrium
position and
experiences a restoring force approximately described by Hooke's
law. Examples
of simple harmonic oscillators include: a mass attached to a
spring, a molecule inside a solid, a car stuck in a ditch being
``rocked out'' and a pendulum.
Note:

The negative sign in Hooke's law ensures that the force is always
opposite to the direction
of the displacement and therefore back towards the equilibrium
position (i.e. a restoring force).

The constant k in Hooke's law is traditionally called the
spring constant for the system, even when the restoring force
is not
provided by a simple spring.
 The motion of any simple harmonic oscillator is
completely characterized by two quantities: the amplitude, and the
period (or frequency).
Next: Elastic Potential Energy
Up: Vibrations and Waves
Previous: Vibrations and Waves
wwwadmin@theory.uwinnipeg.ca
10/9/1997