10.2. Mass on a Spring http://www.ck12.org
10.2 Mass on a Spring
Objective
The student will:
- Solve problems dealing with simple harmonic motion.
Vocabulary
- amplitude:The maximum distance from equilibrium of an object’s periodic motion.
- frequency: The reciprocal of the periodf=T^1.
- Hertz: Units used in place of revolutions per second, as well as cycles per second. Hertz is equivalent
to^1 scycle and revolution and has no SI units. - period:The amount of time it takes an object to repeats its motion.
Introduction
A mass on a spring is the simplest case of simple harmonic motion (SHM).
InFigure10.6, the equilibrium point of the mass on the spring is labeled 0. This is the rest position of the spring,
when it is neither contracting or expanding.
When the mass is pulled sideways and released, the spring will cause the mass to move back toward its equilibrium
position. The tension forceFaof the spring upon the mass is, therefore, directed toward the equilibrium position and
is proportional to the displacement of the mass (recall Hooke’s Law). The mass will pass through the equilibrium
position and as it does, the spring will begin to slow the mass down until it is brought to rest at position –x, opposite
where the mass started.
After the mass passes its equilibrium position, forceFbof the spring upon the mass changes direction so that it keeps
pointing toward the equilibrium position. In other words, the force on the mass by the spring is always directed
toward the equilibrium position of the mass. We call this force a restoring force.
These observations lead us to the conditions for simple harmonic motion:
An object performing SHM must have a restoring force acting upon it that seeks to return it to its equilibrium
position. The magnitude of that force is directly proportional to the object’s displacement. That is,F=−kx, where
the negative sign indicates that the restoring force and displacement are oppositely directed andkis a constant of
proportionality.