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chapter13.3_13.5_slides

# chapter13.3_13.5_slides - Many aspects of the simple...

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12/1/2009 1 Many aspects of the simple harmonic motion can be understood by analyzing the uniform circular motion Consider an object doing a uniform circular motion - radius is A - tangential speed is v 0 (constant) The x-component of the tangential velocity (absolute value) ) sin( 0 v v x A x A 2 2 ) sin( x v 2 2 0 x A A v v x C=v 0 /A is a constant. Speed of an object doing simple harmonic motion: here . There is clear similarity between the x-component of the velocity of a uniform circular motion and the velocity of the simple harmonic motion. ( flash animation ) 2 2 2 2 0 x A C x A A v v x x v ) ( ) ( 2 2 2 2 x A C x A m k v m k C

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2 Period of uniform circular motion: For simple harmonic motion, the maximum speed v 0 and vibration amplitude A is related by (energy conservation) Substituting v 0 into (1) k m T 2 A m k v 0 2 2 0 2 1 2 1 kA mv ) 1 ( 2 0 v A speed tangential nce circumfere T k m A m k A v A T 2 2 2 0 Period is independen t of vibration amplitude (flash demo) Frequency: (number of cycles/second) - Unit: 1/second or Hertz, Hz The angular frequency k ƒ 2
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chapter13.3_13.5_slides - Many aspects of the simple...

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