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Unformatted text preview: Chapter 10 Simple Harmonic Motion and Elasticity 10.1 The Ideal Spring and Simple Harmonic Motion x k F Applied x = spring constant Units: N/m 10.1 The Ideal Spring and Simple Harmonic Motion Example 1 A Tire Pressure Gauge The spring constant of the spring is 320 N/m and the bar indicator extends 2.0 cm. What force does the air in the tire apply to the spring? 10.1 The Ideal Spring and Simple Harmonic Motion ( 29 ( 29 N 4 . 6 m 020 . m N 320 = = = x k F Applied x 10.1 The Ideal Spring and Simple Harmonic Motion Conceptual Example 2 Are Shorter Springs Stiffer? A 10coil spring has a spring constant k . If the spring is cut in half, so there are two 5coil springs, what is the spring constant of each of the smaller springs? 10.1 The Ideal Spring and Simple Harmonic Motion HOOKE’S LAW: RESTORING FORCE OF AN IDEAL SPRING The restoring force on an ideal spring is x k F x = 10.2 Simple Harmonic Motion and the Reference Circle t A A x ϖ θ cos cos = = DISPLACEMENT 10.2 Simple Harmonic Motion and the Reference Circle t A A x ϖ θ cos cos = = 10.2 Simple Harmonic Motion and the Reference Circle period T: the time required to complete one cycle frequency f: the number of cycles per second (measured in Hz) T f 1 = T f π π ϖ 2 2 = = amplitude A: the maximum displacement 10.2 Simple Harmonic Motion and the Reference Circle VELOCITY t A v v v T x ϖ ϖ θ sin sin max = = 10.2 Simple Harmonic Motion and the Reference Circle Example 3 The Maximum Speed of a Loudspeaker Diaphragm The frequency of motion is 1.0 KHz and the amplitude is 0.20 mm. (a)What is the maximum speed of the diaphragm? (b)Where in the motion does this maximum speed occur? 10.2 Simple Harmonic Motion and the Reference Circle t A v v v T x ϖ ϖ θ sin sin max = = (a) ( 29 ( 29 ( 29 ( 29 s m 3 . 1 Hz 10 . 1 2 m 10 20 . 2 3 3 max =...
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This note was uploaded on 02/20/2010 for the course PHYSC 210 taught by Professor Uscinski during the Summer '09 term at American.
 Summer '09
 Uscinski

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