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The initial position, velocity, and acceleration of an object moving in simple harmonic motion are xi, Vi, and a;; the angular frequency of oscillation is w. (a) Show that the position and velocity of the object for all time can be written as x(t) = x; cos(wt) + sin(wt) v(t) : = -xjw sin(wt) + v; cos(wt). (b) Using A to represent the amplitude of the motion, show that v? – ax = v} – a;x; = w² A².

The initial position, velocity, and acceleration of an object moving in simple harmonic motion are xi, Vi, and a;; the angular frequency of oscillation is w. (a) Show that the position and velocity of the object for all time can be written as x(t) = x; cos(wt) + sin(wt) v(t) : = -xjw sin(wt) + v; cos(wt). (b) Using A to represent the amplitude of the motion, show that v? – ax = v} – a;x; = w² A².

College Physics
College Physics
11th Edition
ISBN:9781305952300
Author:Raymond A. Serway, Chris Vuille
Publisher:Raymond A. Serway, Chris Vuille
Chapter1: Units, Trigonometry. And Vectors
Section: Chapter Questions
Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...
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The initial position, velocity, and acceleration of an object moving in simple harmonic motion are x¡, Vi, and a;; the angular frequency of oscillation is w. (a) Show that the position and velocity of the object for all time can be written as Vi x(t) = x; cos(wt) + () sin(wt) v(t) = –xjw sin(wt) + v; cos(wt). (b) Using A to represent the amplitude of the motion, show that v2 – ax = vý – a;X; = w²A². ах -
Transcribed Image Text:The initial position, velocity, and acceleration of an object moving in simple harmonic motion are x¡, Vi, and a;; the angular frequency of oscillation is w. (a) Show that the position and velocity of the object for all time can be written as Vi x(t) = x; cos(wt) + () sin(wt) v(t) = –xjw sin(wt) + v; cos(wt). (b) Using A to represent the amplitude of the motion, show that v2 – ax = vý – a;X; = w²A². ах -
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