Simple harmonic motion and uniform circular motion

Simple harmonic motion and uniform circular motion

Simple harmonic motion can be considered to be the one-dimensional projection of uniform circular motion.

Physics

Keywords

simple harmonic motion, circular motion, amplitude, velocity, acceleration, circular path, spring, period, frequency, time-dependence of amplitude, time-dependence of velocity, time-dependence of acceleration, angular frequency, angular velocity, periodicity, motion, mechanics, mass, physics, vector

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The velocity of harmonic motion can be determined from the circumferential speed of the uniform circular motion projected on the y-axis. Using:

and

we can determine the time-dependence of velocity from the triangle shown in the figure:

The magnitude and direction of the velocity of harmonic motion change periodically. The magnitude of velocity is the highest when it moves toward the equilibrium position, and it is 0 at the two points of oscillation.

The acceleration of the harmonic motion can be determined from the centripetal acceleration of the uniform circular motion projected on the y-axis.

and

we can determine the time-dependence of velocity from the triangle shown in the figure:

The acceleration of harmonic motion is highest at the two points of oscillation, and the lowest at the equilibrium position. The acceleration vector always points toward the equilibrium position.

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