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Monday, June 23, 2008

Simple Harmonic Motion

(1) The middle picture is what a mass on a spring would do if it were sliding on a completely frictionless surface.

(2) Notice how the mass is always directly below the red circle. That mass on the spring represents the X-component (i-vector) of the circular trajectory of the top picture.

(3) Notice how the graph on the bottom shows how the kinetic energy "K" plus the potential spring energy "U" is always constant for the system (the sum of the energies is always equal to E-total). That is representative of the conservation of energy for the spring-mass system, the middle picture.

(4) Simple Harmonic Motion, or systems that oscillate in a sinousoidal fashion, can be used to model/represent a lot of different things in physics .... orbits, springs, the magnetic core in stereo speakers, pendulums, electron resonances, sound waves, light waves, antennas, or anything else that oscillates at a specified frequency.

The parametric equation for the top animation is:
{x(t),y(t)}= [Ao*cos(kt)] i + [Ao*sin(kt)] j

where Ao => radius; k=> angular velocity