Harmonic MotionHarmonic Motion

Not Linear Motion—been Not Linear Motion—been there, done thatthere, done that

Harmonic Motion - definitionHarmonic Motion - definition

Motion that repeatsMotion that repeats Motion that has a cycleMotion that has a cycle Motion that swings back and forthMotion that swings back and forth

Harmonic Motion - examplesHarmonic Motion - examples

• Person swinging on a swing• Water cycle

• Motion of a yoyo• Rotation of the earth on its axis

Can you think of others?

Harmonic motion definitionsHarmonic motion definitions

CycleCycle – – Building block of harmonic motion; unit Building block of harmonic motion; unit of motion that repeats over and overof motion that repeats over and over

PeriodPeriod – – Time needed to repeat one cycleTime needed to repeat one cycle

SystemSystem – – A group we choose that includes all the A group we choose that includes all the things we are interested inthings we are interested in

More definitionsMore definitions OscillatorOscillator – –

A system that shows harmonic motion A system that shows harmonic motion (A (A pendulum is an oscillator.)pendulum is an oscillator.)

Examples of other oscillators:Examples of other oscillators:- Light and sound come from oscillations- Light and sound come from oscillations- Music and musical instruments are - Music and musical instruments are oscillatorsoscillators- Cell phones, radio broadcasts, clocks make - Cell phones, radio broadcasts, clocks make use of oscillationsuse of oscillations

Characteristics of cyclesCharacteristics of cycles

Period: Period: TimeTime for one cycle; how long a for one cycle; how long a cycle lasts; period (of time) is usually cycle lasts; period (of time) is usually measured in seconds.measured in seconds.

Frequency: Frequency: number of cycles per secondnumber of cycles per second

Hertz--unit of frequency (one hertz is Hertz--unit of frequency (one hertz is one cycle/second)one cycle/second)

Relationship between Period and Frequency:Relationship between Period and Frequency:

F = 1 / tF = 1 / t t = 1 / Ft = 1 / F

Calculate the frequency of a Calculate the frequency of a pendulum that has a period of pendulum that has a period of

¼ second.¼ second.

Solution:

1.You are asked for frequency.

2.You are given period.

3.Relationship is F = 1 / t

4.Substitute numbers:F = 1 / 0.25 sec = 4 hz

Characteristics of cyclesCharacteristics of cycles

AmplitudeAmplitude

how big the cycle is; the maximum distance how big the cycle is; the maximum distance an object moves from its rest position (we an object moves from its rest position (we can vary the amplitude of a pendulum)can vary the amplitude of a pendulum)

If you know the period If you know the period oror frequency frequency andand the the amplitude, then you have defined the amplitude, then you have defined the motion of the oscillator.motion of the oscillator.

DampingDamping The slowing down of the motion; The slowing down of the motion; loss in amplitude over timeloss in amplitude over time

FA

Harmonic or not?Harmonic or not?

1.1. A moving rocking chairA moving rocking chair

2.2. Bike ride to a friend’s houseBike ride to a friend’s house

3.3. Bike pedals during #2Bike pedals during #2

4.4. Your schedule at CJHSYour schedule at CJHS

Check Your UnderstandingCheck Your Understanding

Obtain a colored card stack and be Obtain a colored card stack and be ready to hold up the correct card ready to hold up the correct card representing the correct answer for representing the correct answer for the following questions.the following questions.

#1#1

The characteristics of a cycle are:The characteristics of a cycle are:

A. Period, Cycle, OscillationA. Period, Cycle, Oscillation

B. Period, Cycle, FrequencyB. Period, Cycle, Frequency

C. Period, Frequency, AmplitudeC. Period, Frequency, Amplitude

D. Period, Frequency, OscillationD. Period, Frequency, Oscillation

#1#1

The characteristics of a cycle are:The characteristics of a cycle are:

A. Period, Cycle, OscillationA. Period, Cycle, Oscillation

B. Period, Cycle, FrequencyB. Period, Cycle, Frequency

C. Period, Frequency, AmplitudeC. Period, Frequency, Amplitude

D. Period, Frequency, OscillationD. Period, Frequency, Oscillation

#2#2

If the frequency is 0.5 cycles/second, If the frequency is 0.5 cycles/second,

then the period is:then the period is:

A. 2 seconds A. 2 seconds

B. 0.25 secondsB. 0.25 seconds

C. 2 hertzC. 2 hertz

D. 0.25 hertzD. 0.25 hertz

#2#2

If the frequency is 0.5 cycles/second, If the frequency is 0.5 cycles/second,

then the period is:then the period is:

A. 2 secondsA. 2 seconds

B. 0.25 secondsB. 0.25 seconds

C. 2 hertzC. 2 hertz

D. 0.25 hertzD. 0.25 hertz

#3#3

If the period is 5 seconds, then the If the period is 5 seconds, then the

frequency is:frequency is:

A. 0.2 newtons A. 0.2 newtons

B. 0.2 hertz B. 0.2 hertz

C. 0.2 watts C. 0.2 watts

D. 0.2 seconds D. 0.2 seconds

#3#3

If the period is 5 seconds, then the If the period is 5 seconds, then the

frequency is:frequency is:

A. 0.2 newtons A. 0.2 newtons

B. 0.2 hertzB. 0.2 hertz

C. 0.2 watts C. 0.2 watts

D. 0.2 seconds D. 0.2 seconds