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Periodic motion Frequency Period. Periodic motion – Any motion that repeats itself. Simple harmonic motion. Figure 13-1 A Mass Attached to a Spring Undergoes Simple Harmonic Motion About x = 0. Sine and cosine curves. - PowerPoint PPT Presentation
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•Periodic motion•Frequency•Period
•Periodic motion –Any motion that repeats itself.
Period time required for one cycle of a periodic motionSI unit=s
T
1
Frequency is the number of oscillations per unit time
SI unit=sec
f
cycles s Hzond
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 fT
radUnit ss
Position2cos( ) cosx A t A tT
Velocity,
maxsin( ) v A t v Amunits
Acceleration2
2max
2
cos( )a A t
a Amunits
Period of a mass on a spring
2 kTm
Period of a pendulum
2 LTg
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
1 cos ( )21 sin ( )2
U kA t
K kA t
Total energy of a mass on a spring.
212
E kA
Total energy of a pendulum
max1 cosE mgL