http://www.ck12.org Chapter 10. Periodic Motion
http://www.animations.physics.unsw.edu.au/jw/SHM.htm
FIGURE 10.3
Though the typical (calculus-based) mathematical derivation showing the relationship between the projection of
uniform circular motion and simple harmonic motion is beyond the scope of this book, we will nonetheless give a
plausible mathematical argument for it later.
Conditions for Simple Harmonic Motion
For the moment, we state without proof that the motion of a mass (the block inFigure10.4, for example) moving
back and forth on the end of a spring, is the same as the projected motion of the Ferris wheel car inFigure10.3.
FIGURE 10.4
InFigure10.4, the equilibrium point of the mass on the spring is labeled 0. The spring is assumed to have negligible
mass and the mechanical energy of the mass-spring system is assumed to be conserved. (Unless otherwise stated, we
will always assume that the mass of the spring is negligible and the mechanical energy of the system is conserved.)
When the mass is pulled sideways and released, the spring will cause the mass to move back toward its equilibrium
position. The tension forceFaof the spring upon the mass is, therefore, directed toward the equilibrium position and