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

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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