Simple Harmonic Motion

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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.
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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.

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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.
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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. 
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Hearbeat Oscillating mass on a
spring
Periodic Motion Simple Harmonic Motion
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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.
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Simple Harmonic Motion
When there is a restoring force, F -kx, simple
harmonic motion occurs.
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Amplitude
Amplitude is the magnitude of the maximum
displacement.
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Period, T
For any object in simple harmonic motion, the
time required to complete one cycle is the period
T.
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Frequency, f
The frequency f of the simple harmonic motion is
the number of cycles of the motion per second.
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Exercise on Simple Harmonic Motion
Q1. What is the amplitude?Q2. What is the
period? Q3. What is the frequency?
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Graphs of position, velocity, and acceleration

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