Simple Harmonic Motion
The single most important concept in the study of waves and sound is
that of simple harmonic motion (SHM).
Simple harmonic motion is typified by the motion of a mass on a
spring when it is subject to the linear elastic restoring force given by
Hooke's Law. The motion is sinusoidal in time and demonstrates a
single resonant frequency.
Periodic Motion
Motion that repeats in a regular pattern
over and over again is called periodic
motion.
Simple harmonic motion is a specific type
of periodic motion that has a simple sine
or cosine wave shape.
Simple Harmonic Motion (SHM)
Physicists like simple harmonic motion because every example of SHM is
based on the same underlying physical principle and all examples of
SHM have the same, very straightforward, mathematical description.
What is the physical principle? SHM occurs around an equilibrium
position when a mass is subject to a linear restoring force. A linear
restoring force is one that gets progressively larger with displacement
from the equilibrium position. The best example of this is a spring. The
more you stretch a spring the larger the force trying to get the spring back
to its original shape.
Position VS. Time graph
What is the simple mathematical form of SHM
motion?
The displacement of the oscillating mass
varies sinusoidally as a function of time.
Hearbeat Oscillating mass on a spring
Periodic Motion Simple Harmonic Motion
HOOKE'S LAW
The restoring force of an ideal spring is given by,
where k is the spring constant and x is the
displacement of the spring from its
unstrained length. The minus sign indicates
that the restoring force always points in a
direction opposite to the displacement of
the spring.
Simple Harmonic Motion
When there is a restoring force, F = -kx, simple harmonic
motion occurs.
Amplitude
Amplitude is the magnitude of the maximum displacement.
Period, T
For any object in simple harmonic motion, the time
required to complete one cycle is the period T.
Frequency, f
The frequency f of the simple harmonic motion is the
number of cycles of the motion per second.
Exercise on Simple Harmonic
Motion
Q1. What is the amplitude?
Q2. What is the period?
Q3. What is the frequency?
Graphs of position, velocity, and
acceleration
http://physics.bu.edu/~duffy/semester1/c18_SHM_graphs.html