Harmonic Motion Not Linear Motion—been there, done that

Harmonic Motion - definition Motion that repeats Motion that has a cycle Motion that swings back and forth

Harmonic 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 definitions Cycle – Cycle – Building block of harmonic motion; unit of motion that repeats over and over Period – Period – Time needed to repeat one cycle System – System – A group we choose that includes all the things we are interested in

More definitions Oscillator – Oscillator – A system that shows harmonic motion (A pendulum is an oscillator.) Examples of other oscillators: Examples of other oscillators: - Light and sound come from oscillations - Music and musical instruments are oscillators - Cell phones, radio broadcasts, clocks make use of oscillations

Characteristics of cycles Period: Time for one cycle; how long a cycle lasts; period (of time) is usually measured in seconds. Period: Time for one cycle; how long a cycle lasts; period (of time) is usually measured in seconds. Frequency: number of cycles per second Frequency: number of cycles per second Hertz--unit of frequency (one hertz is one cycle/second) Relationship between Period and Frequency: F = 1 / tt = 1 / F

Calculate the frequency of a pendulum that has a period of 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 cycles Amplitude how big the cycle is; the maximum distance an object moves from its rest position (we can vary the amplitude of a pendulum) If you know the period or frequency and the amplitude, then you have defined the motion of the oscillator. Damping The slowing down of the motion; loss in amplitude over time FA

Harmonic or not? 1. A moving rocking chair 2. Bike ride to a friend’s house 3. Bike pedals during #2 4. Your schedule at CJHS

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

#1 The characteristics of a cycle are: A. Period, Cycle, Oscillation B. Period, Cycle, Frequency C. Period, Frequency, Amplitude D. Period, Frequency, Oscillation

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#2 If the frequency is 0.5 cycles/second, then the period is: A. 2 seconds B seconds C. 2 hertz D hertz

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#3 If the period is 5 seconds, then the frequency is: A. 0.2 newtons B. 0.2 hertz C. 0.2 watts D. 0.2 seconds

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