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•Periodic motion•Frequency•Period
•Periodic motion –Any motion that repeats itself.
Period time required for
one cycle of a periodic motion
SI unit=s
T
1
Frequency is the number of oscillations per unit time
SI unit=sec
f
cycless Hz
ond
Simple harmonic motion
Figure 13-1A Mass Attached to a Spring
Undergoes Simple Harmonic Motion About x = 0
Sine and cosine curves
Figure 13-2Displaying Position Versus Time for Simple Harmonic Motion
Figure 13-3Simple Harmonic Motion as a Sine or a Cosine
Connection to uniform circular
motion
Figure 13-4The Relationship Between Uniform Circular Motion
and Simple Harmonic Motion
Equations that apply to circular motion
also apply to simple harmonic motion.
Angular frequency
1
2Angular frequency= 2 f
Trad
Unit ss
Position2
cos( ) cosx A t A tT
Velocity,
maxsin( ) v A t v A
munit
s
Acceleration2
2max
2
cos( )a A t
a A
munit
s
Period of a mass on a spring
2k
Tm
Period of a pendulum
2L
Tg
Energy conservation
Figure 13-10Energy as a Function of Position in Simple Harmonic Motion
Energy conservation for a mass on a spring
2 2
2 2
1cos ( )
21
sin ( )2
U kA t
K kA t
Total energy of a mass on a spring.
21
2E kA
Total energy of a pendulum
max1 cosE mgL