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Harmonic Motion

Repeats itself over and over againExamples?

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Cycle

• Building block of harmonic motion

• Unit of motion that repeats over and over

• Harmonic motion = sequence of cycles

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Harmonic motion in Nature

• Examples?– Heart– Solar system– Electrons moving around atom– El Nino, La Nina

• Oscillators- systems that show harmonic motion

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Harmonic motion in art and music

• Examples?

• Music

• Color

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Harmonic Motion in technology

• Cell phones

• FM radio

• Telling time - Grandfather clocks, atomic clocks

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Harmonic Motion

• Period- time to complete one cycle

• Frequency- number of cycle per second

• One cycle per second= a hertz (Hz)

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Period and Frequency

T= 1/f f= 1/T

T= Period (seconds)f= frequency in Hz

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• Amplitude- size of the cycle

• Damping- gradual loss of amplitude (friction)

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Graphing Harmonic motion

• Use positive and negative values

• Start zero halfway up y-axis

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Amplitude from graph

• Half the distance between the highest and lowest points on the graph

• Amplitude = 1/2 (high-low)

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Period from graph

• Time difference between the beginning of the cycle and the end

• Period = (ending time- beginning time)

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Examples of Oscillators

• Pendulum

• Mass on a spring

• Vibrating string