Friday, July 17, 2015

Twirl and SHM

This is the third way a negative particle and a positive particle are bounded.  In this case the negative particle with less energy density is accelerated into the positive particle's \(\psi\) cloud.


This particle is in circular motion.  It is not in Harmonic Oscillation, both its KE and PE are constant.  The negative particle is always at a distance \(x\) from the center of the positive particle.  This negative particle experiences a force that move it towards region of denser \(\psi\) and away from less dense \(\psi\) in the positive particles.  In the region \(x\gt x_z\), increasing \(x\) decreases \(\psi\).  As such \(F\) in the diagram marks the direction of the force on the negative particle.  This force provides the centripetal force that sustains circular motion.  The diagram on the right gives the top view.

This is the negative particle in oscillation about \(x=x_z\) where \(\psi=\psi_{max}\),


At equal distance from \(x=x_z\) inside and outside of the \(\psi_{max}\) circle, \(\psi\) due to the positive particle is the same smaller value.  The negative particle is attracted to \(\psi_{max}\), passes \(\psi_{max}\) with a certain velocity, beyond \(\psi_{max}\) it experiences a retarding force,  At the deepest penetration into the positive particle, the negative particle has zero velocity and is accelerated back toward \(\psi_{max}\).  This is simple harmonic motion.