Simple Harmonic Motion


The red particle follows a circular path with radius R in anti-clock wise direction (considered positive) with a uniform speed. Its x and y projections are shown in light-blue and orange respectively. If the angular position of the red particle is denoted by q then its x and y coordiantes are R cos φ and R sin φ (with x to the right, y upward, and origin at the center of the circle). Since the motion of the particle round the circle is uniform, q = ωt + φ (where ω is the angular velocity and φ is the initial angular position of the red particle). In the applet, φ = 0 and q is shown by the small, blue-filled arc at the center. The phase is reset to zero after every revolution. In practice it would increase by 2π radians for every revolution.

The motion of the light-blue particle can be represented as

x = Rcos(ωt + φ)

and that of the orange particle as

y = Rsin(ωt + φ)

Notice how the velocity vectors of the light-blue and orange particles differ.


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