Simple Harmonic Motion
…an introduction.
• A periodic (repeating) motion that is
the result of a restoring force.
• The restoring force is proportional to
the object’s displacement from the
rest position.
• The restoring force always acts
toward the rest position (equilibrium).
• One complete oscillation of an
object undergoing periodic motion;
when an object undergoing periodic
motion has returned to its initial
state (position and velocity), it has
completed one cycle.
• The time it takes for an object
in SHM to undergo one complete
cycle.
• Symbol: T
• Units: seconds, minutes, days,
etc.
• The number of cycles that occur per
unit of time (usually per second).
• Symbol: f (or ν—Greek letter “nu”)
• Units: hertz (Hz), sec-1, rev/sec, etc.
• T and f are inverses of one another.
1
T
f
1
f
T
• The maximum displacement of an
object from its equilibrium position.
• Symbol: A
• Units: meters, cm, mm, nm, km, etc.
1 amplitude
1 amplitude
1 amplitude
1 amplitude
During one cycle, an object in SHM
travels a total distance equal to 4
times its amplitude.
Example Problem #1
A 16.3 kg mass oscillates at the
end of a spring, completing one
cycle every 2.10 s. What is
the spring constant of the
spring?
Example Problem #2
The frequency of vibration of a
simple pendulum on Earth is
0.484 Hz. Find its length.