Introduction to the Model
Description and Assumptions
This model applies to position of a single point particle, or to the angular position of a rigid body, which is constrained to one dimension and experiences a restoring force that is linearly proportional to its displacement from an equilibrium position. This form for the force or torque implies that the equation of motion for the point particle or rigid body will have the form:
\begin
[ a = \frac{d^
x}{dt^{2}} = - \omega_
^
x ]\end
or
\begin
[ \alpha = \frac{d^
\theta}{dt^{2}} = -\omega_
^
\theta] \end
.
As a consequence of this characteristic equation, the position, velocity, and acceleration (or the angular equivalents) will each be sinusoidal functions of time. Simple harmonic motion is sometimes abbreviated SHM, or referred to as "Simple Harmonic Oscillation" (SHO).
Learning Objectives
Students will be assumed to understand this model who can: