Caption: An animation of a simple harmonic oscillator exhibiting simple harmonic motion.

Features:

1. The illustrated dynamical variable vectors:
   1. x is position measured from the zero position which is the mechanical equilibrium point (which is discussed below).
   2. v is velocity.
   3. a is acceleration.

   The x, v, and a arrow symbols give the directions of the vectors and their lengths, the magnitudes.

2. In the case of this animation, the simple harmonic oscillator is an object (i.e., a block) and a spring.

   The system is ideal, and so there is NO dissipation of mechanical energy to waste heat by friction external at the contact surfaces or internal to the spring.

3. In simple harmonic motion an object is subject only to the Hooke's law force (i.e., the ideal spring force) F = -kx, where k is the spring constant and the negative sign means the force vector points opposite to the position vector.

   The Hooke's law force always pulls the object toward the mechanical equilibrium point where the Hooke's law force is zero.

4. Pulling in the direction of motion speeds up the object and changes its Hooke's law force potential energy into kinetic energy.

   Pulling in opposite the direction of motion slows down the object and changes its kinetic energy into Hooke's law force potential energy.

   The energy keeps switching back and and forth between kinetic energy (1/2)mv**2 and Hooke's law force potential energy (1/2)kx**2, where m is the object and k is again the spring constant.

   The total mechanical energy E is conserved: i.e., E = (1/2)mv**2 + (1/2)kx**2 is constant.

5. Without dissipation to convert the mechanical energy into waste heat, simple harmonic motion is perpetual.

   If there was dissipation, the system would exhibit damped harmonic motion and eventually would stop moving with the object at rest at the mechanical equilibrium point.