\(\psi\), \(F\) and \(q\) all adds up. At the plateau, for \(Z\) number of particles,
\(ln(cosh(\cfrac { G }{ \sqrt { 2{ mc^{ 2 } } } } x_z))\rightarrow Z*ln(cosh(\cfrac { G }{ \sqrt { 2{ mc^{ 2 } } } } x_z))=Z\)
So,
\(\psi_n\rightarrow Z*\psi_n\)
and under the strict condition,
\(\cfrac { \psi _{ d } }{ m } =2{ c^{ 2 } }cos(\theta )ln(cosh(\cfrac { G }{ \sqrt { 2{ mc^{ 2 } } } } x_z))\)
from the post "Twirl Plus SHM, Spinning Coin" dated 17 Jul 2015, \(\psi_d\) is the displacement of \(\psi\) in the containing \(\psi\) cloud that performs \(SHM\). So,
\(\cfrac { \psi _{ d } }{ m }\rightarrow Z*\cfrac { \psi _{ d } }{ m } \)
but \(\psi_{max}\) is still one particle, \(n=77\) (as defined),
\(\psi_{max}=1\)
with \(m\,\,or\,\,m_{\rho}=\cfrac{1}{2c^2}*\cfrac{1}{2.4438}\)
so,
\(v^{ 2 }_{ { max } }=-Z*\cfrac { \psi _{ d }}{ m } Z*\cfrac { \psi _{ n } }{ \psi _{ max } }\ e^{ \psi _{ max } }\left( { e^{ 2\psi _{ max } }-1 } \right) ^{ 1/2 }\)
thus,
\(v^{ 2 }_{ { max } }\rightarrow Z^2*v^{ 2 }_{ { max } }\)
Note: I have a few missing posts on the new mode of oscillations; of SHM within \(\psi\).
\(\psi_{d}=\psi_{max}-\psi_n\) --- (*)
is only for a particle of \(\psi_{max}\) receiving a particle of \(\psi_n\), as the scenario is developed in the post "Twirl Plus SHM, Spinning Coin" dated 17 Jul 2015. \(\psi_d\) is the displaced \(\psi\) in \(SHM\) in general and is not restricted to (*).
Note: If \(\psi_{max}\) is also scaled then all the particles in the expression for \(v_{max}\) is scaled by \(Z\) which lead back to the situation without scaling.
