Relation Between Simple Harmonic and Uniform Circul

Relation Between Simple Harmonic and Uniform Circul -...

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Relation Between Simple Harmonic and Uniform Circul ar Motion Through our study of simple harmonic oscillations we have used sine and cosine functions, and talked about angular frequency. It seems natural that there should be some connection between simple harmonic motion and uniform circular motion . In fact, there is an astonishingly simple connection that can be easily seen. Consider a particle traveling in a circle of radius R centered about the origin, shown below: Figure %: A particle, starting at point P, travelling in uniform circular motion with a radius of R, and angular velocity σ . What is the x coordinate of the particle as it goes around the circle? The particle is shown at point Q, at which it is inclined an angle of θ from the x -axis. Thus the position of the particle at that point is given by: x = R cos θ However, if the particle is traveling with a constant angular velocity σ , then we can express θ as: θ = σt . In addition, the maximum value that x can take is at the point (R,0), so we can state that
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