CHAPTER 23CHAPTER 23WAVESWAVES

23.123.1

Harmonic MotionHarmonic Motion

pp. 554-561pp. 554-561

23.1 Harmonic motion23.1 Harmonic motion

A.A. Linear motionLinear motion gets us from one gets us from one place to place to another.another.

B.B. Harmonic Harmonic motionmotion is motion is motion that repeats that repeats over and over.over and over.

23.1 Harmonic motion23.1 Harmonic motion• A A pendulumpendulum is a device that swings is a device that swings

back and forth.back and forth.• A A cyclecycle is one unit of harmonic motion. is one unit of harmonic motion.

• One cycle = 1/secondOne cycle = 1/second

23.1 Oscillators23.1 Oscillators

• An An oscillator oscillator is a is a physical system that physical system that has repeating cycles has repeating cycles or harmonic motion.or harmonic motion.

• Systems that Systems that oscillate move back oscillate move back and forth around a and forth around a center or center or equilibriumequilibrium position.position.

23.1 Oscillators23.1 Oscillators• A A restoring forcerestoring force is any force that is any force that

always acts to pull a system back always acts to pull a system back toward equilibrium.toward equilibrium.

23.1 Harmonic motion23.1 Harmonic motion• Harmonic motion can be fast or slow, Harmonic motion can be fast or slow,

but speed constantly changes during but speed constantly changes during its cycle. its cycle.

• We use We use periodperiod and and frequencyfrequency to to describe how quickly cycles repeat describe how quickly cycles repeat themselves.themselves.

• The time for one cycle to occur is The time for one cycle to occur is called a called a periodperiod..

23.1 Harmonic motion23.1 Harmonic motion• The The frequencyfrequency is the is the

number of complete number of complete cycles per second. cycles per second.

• Frequency and period Frequency and period are are inversely relatedinversely related. .

• One cycle per second is One cycle per second is called a called a hertz,hertz, abbreviated (Hz).abbreviated (Hz).

Solving ProblemsSolving Problems

• The period of an The period of an oscillator is 2 oscillator is 2 minutes. minutes.

• What is the frequency What is the frequency of this oscillator in of this oscillator in hertz?hertz?

1.1. Looking for: Looking for: – ……frequency in hertzfrequency in hertz

2.2. GivenGiven– ……period = 2 minperiod = 2 min

3.3. Relationships:Relationships:– ……60 s = 1 min60 s = 1 min

– … … f f = 1/= 1/TT4.4. SolutionSolution

– … … f f = 1/120 s= 1/120 s

Solving ProblemsSolving Problems

f = .008 Hz

23.1 Period and Frequency23.1 Period and Frequency

•Complete 23.1 Period and Complete 23.1 Period and Frequency WS.Frequency WS.

•Show ALL work on a Show ALL work on a separate sheet of paper.separate sheet of paper.

23.1 Amplitude23.1 Amplitude• AmplitudeAmplitude describes describes

the “size” of a cycle.the “size” of a cycle.

• The amplitude is the The amplitude is the maximum distance maximum distance the oscillator moves the oscillator moves away from its away from its equilibriumequilibrium position.position.

23.1 Amplitude23.1 Amplitude

• The amplitude of a water wave is found by The amplitude of a water wave is found by measuring the distance between measuring the distance between the the highest and lowest points on the wave. highest and lowest points on the wave. This is called the wave height.This is called the wave height.

• The amplitude is The amplitude is halfhalf this distance this distance..

23.1 Amplitude23.1 Amplitude

• A pendulum with A pendulum with an amplitude of an amplitude of 20 degrees swings 20 degrees swings 20 degrees away 20 degrees away from the center in from the center in either direction.either direction.

23.1 Damping23.1 Damping• Friction slows a pendulum down, just Friction slows a pendulum down, just

as it slows all motion.as it slows all motion.

• DampingDamping is the gradual loss of is the gradual loss of amplitude.amplitude.

23.1 Graphs of harmonic 23.1 Graphs of harmonic motionmotion • A graph is a good A graph is a good

way to show way to show harmonic motion harmonic motion because because you can you can quickly recognize quickly recognize cycles. cycles.

• Graphs of linear Graphs of linear motion motion do not do not show cycles.show cycles.

HARMONIC MOTION HARMONIC MOTION GRAPHSGRAPHS

•Complete 23.1 Complete 23.1 Harmonic Motion Graphs Harmonic Motion Graphs WSWS

23.1 Natural frequency 23.1 Natural frequency and resonanceand resonance

• The The natural natural frequencyfrequency is the is the frequency (or period) frequency (or period) at which a system at which a system naturally oscillates. naturally oscillates.

• Every system that Every system that oscillates oscillates has a has a natural frequencynatural frequency..

23.1 Natural frequency 23.1 Natural frequency and resonanceand resonance• You can get a swing You can get a swing

moving by pushing moving by pushing it at the right time it at the right time every cycle.every cycle.

• A force that is A force that is repeated over and repeated over and over is called a over is called a periodic forceperiodic force..

23.1 Natural frequency 23.1 Natural frequency and resonanceand resonance

• ResonanceResonance happens happens when a periodic force when a periodic force has the same has the same frequency frequency as the as the natural frequencynatural frequency. .

• When each push adds When each push adds to the next one, the to the next one, the amplitude of the amplitude of the motion grows. motion grows.

23.1 Natural frequency 23.1 Natural frequency and resonanceand resonance

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