Simple Harmonic Motion is defined as a periodic motion of a point along a straight line, such that its acceleration is always towards a fixed point in that line and is proportional to its distance from that point. In other words, its acceleration is proportional to the displacement but acts in an opposite direction. Prove algebraically that the motion of a particle defined by x=cos2t + 2sin2t is simple harmonic.
Simple Harmonic Motion is defined as a periodic motion of a point along a straight line, such that its acceleration is always towards a fixed point in that line and is proportional to its distance from that point. In other words, its acceleration is proportional to the displacement but acts in an opposite direction. Prove algebraically that the motion of a particle defined by x=cos2t + 2sin2t is simple harmonic.
Classical Dynamics of Particles and Systems
5th Edition
ISBN:9780534408961
Author:Stephen T. Thornton, Jerry B. Marion
Publisher:Stephen T. Thornton, Jerry B. Marion
Chapter12: Coupled Oscillations
Section: Chapter Questions
Problem 12.22P
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such that its acceleration is always towards a fixed point in that line and is proportional to
its distance from that point. In other words, its acceleration is proportional to the
displacement but acts in an opposite direction. Prove algebraically that the motion of a
particle defined by x=cos2t + 2sin2t is simple harmonic.
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