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4.7 Simple Harmonic Motion

4.7 Simple Harmonic Motion. Many physical periodic happenings can be represented as a sinusoidal function * t is time * is amplitude * is period * is frequency. (maximum displacement). (time for 1 cycle). (# of cycles per unit of time).

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4.7 Simple Harmonic Motion

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  1. 4.7 Simple Harmonic Motion

  2. Many physical periodic happenings can be represented as a sinusoidal function * t is time * is amplitude * is period * is frequency (maximum displacement) (time for 1 cycle) (# of cycles per unit of time) Which do we choose? sine or cosine? - Whichever seems the most appropriate!

  3. Some Examples (but not all the various kinds!) Ex 1) An alternating current can be described by a sinusoidal function where c(t) is the current measured in amperes at t seconds. Find the amplitude, period, & frequency. amp = 18 Per = a b c frequency = 60

  4. Ex 2) The amplitude of a sound wave produced by the note E above middle C is 0.8 and the frequency is 330 cycles per second. Determine the sinusoidal function representing this sound. a = 0.8 frequency = 330  Per =

  5. Ex 3) A weight hanging from the end of a spring is pulled down 12 cm below its resting place & released. It takes 2.4 seconds to complete one cycle. Determine an equation of motion for the weight. Use the cosine function Why cosine? Starts low… not in middle But it’s LOW instead of high How to fix this? Flip over x-axis Make equation negative 12 cm a = 12 (12 down from rest) b = ?

  6. Ex 4) A Ferris wheel is 80 ft. in diameter & rises 86 ft from the ground. Each revolution of the wheel takes 28 seconds. Express the height of a rider as a function of time t if the rider is at the bottom when t = 0. 86 ft diam = 80 ft  radius = 40 ft 40 ft 86 40 ft 6 ft 6 • start @ bottom … • bottom not at 0  at 6 • d = 6 + 40 neg. cos = 46 (middle)

  7. Homework #408 Pg 233 #1, 7, 9, 13, 15, 17, 19, 27, 30, 33, 37, 39

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