Lecture 26
Simple Harmonic Motion
Periodic motion
Periodic motion
A motion is called periodic when the system comes
back to the same situation every time interval
T.
Same position
Same velocity
Period
Examples:
Uniform circular motion
Earth around the Sun
Toy train in a circuit
π
ωπ
=
==
1
Frequency
2
Angular
2
frequency
f
T
Oscillations about an equilibrium position
U
x
When a 1D system is released near a stable
equilibrium point, the motion is periodic: oscillations
between two turnaround points
1
and
2
.
E
1
2
Forbidden region
Forbidden region
Oscillations
SE
Simple Harmonic Motion (SHM)
Simple Harmonic Motion (SHM)
SHM is the oscillatory motion that happens when the
restoring force is proportional to the displacement from
the equilibrium position:
F
∝
–
…or when the potential energy is a quadratic function
of the displacement from the equilibrium position:
U
∝
2
(a parabola)
equivalent to
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View Full DocumentExample of SHM: Spring that obeys Hooke’s law
=−
Fk
x
=
2
1
2
Uk
Oscillations about
= 0
U
E
–x
0
0
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 Fall '06
 Johnson
 Physics, Circular Motion, Force, Simple Harmonic Motion, Quadratic equation

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