Oscillations & waves

[Pages:30]oscillations & waves

physics 111N

periodic motion

! often a physical system will repeat the same motion over and over ! we call this periodic motion, or an oscillation the time it takes for the motion to complete one cycle is called the period, T the number of times the motion repeats in unit time is called the frequency, f

so e.g. if the period is 0.1 s, the frequency is 10 s-1

physics 111N

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simple harmonic motion

! a very special form of periodic motion where the restoring force is proportional to the displacement

! once way to construct such an oscillator is to use a spring obeying Hooke's law

spring compressed

spring at equilibrium

spring extended

physics 111N

x F

x F

x F

4

simple harmonic motion

! a very special form of periodic motion where the restoring force is proportional to the displacement

! once way to construct such an oscillator is to use a spring obeying Hooke's law

physics 111N

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simple harmonic motion

x=-A

the amplitude of motion, A, is the maximum displacement from equilibrium

physics 111N

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simple harmonic motion

0

0

3T4

T4

T2

0

a v

x F

xA x0 xA x=-A

3T4

T4

T2

0

a v

x F

xA x0 xA x=-A

3T4

T4

T2

0

F xA x=-A

a v x

x0 xA

3T4

T4

T2

0

a v x

xA x0 x=-A

F xA

3T4

T4

T2

0

a v x F

xA x0 xA x=-A

3T4

T4

T2

0

xA x=-A

a v x F

x0 xA

3T4

T4

3T4

T4

T2

a

v

x

F

T2

a

v

x

F

physics 111N

xx=-AA x0 xA

xx=-AA x0 xA

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energy in simple harmonic motion

! the elastic restoring force is conservative & there is no friction, so total energy is conserved

when x=A, the block is at rest

x=-A

physics 111N

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energy in simple harmonic motion

! the elastic restoring force is conservative & there is no friction, so total energy is conserved

@

physics 111N

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