Periodic motion Frequency Period. Periodic motion – Any motion that repeats itself

•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