Periodic motion Frequency Period
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Transcript of Periodic motion Frequency Period
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•Periodic motion•Frequency•Period
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•Periodic motion –Any motion that repeats itself.
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Period time required for one cycle of a periodic motionSI unit=s
T
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1
Frequency is the number of oscillations per unit time
SI unit=sec
f
cycles s Hzond
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Simple harmonic motion
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Figure 13-1A Mass Attached to a Spring
Undergoes Simple Harmonic Motion About x = 0
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Sine and cosine curves
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Figure 13-2Displaying Position Versus Time for Simple Harmonic Motion
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Figure 13-3Simple Harmonic Motion as a Sine or a Cosine
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Connection to uniform circular
motion
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Figure 13-4The Relationship Between Uniform Circular Motion
and Simple Harmonic Motion
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Equations that apply to circular motion
also apply to simple harmonic motion.
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Angular frequency
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1
2Angular frequency= 2 fT
radUnit ss
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Position2cos( ) cosx A t A tT
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Velocity,
maxsin( ) v A t v Amunits
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Acceleration2
2max
2
cos( )a A t
a Amunits
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Period of a mass on a spring
2 kTm
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Period of a pendulum
2 LTg
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Energy conservation
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Figure 13-10Energy as a Function of Position in Simple Harmonic Motion
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Energy conservation for a mass on a spring
2 2
2 2
1 cos ( )21 sin ( )2
U kA t
K kA t
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Total energy of a mass on a spring.
212
E kA
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Total energy of a pendulum
max1 cosE mgL