Reaction Time!

Remember the post "My Own Wave equation", dated 20 Nov 2014, where

$\cfrac{\partial \psi}{\partial x}\cfrac{\partial \psi}{\partial t}=\cfrac{c^2p}{\sqrt{2}}.\cfrac{\partial^2\psi}{\partial x^2}.e^{-i\pi/4}$

Why would a force on an object experience a delay in response?  Such a delay was presented as an phase lag one-eight of a period, but what the frequency of the system?

When the object is subjected to a force, this force on the object increases from zero to some value $F$.  The rate of increase of this force is fitted to a sinusoidal $sin(\omega t)$ such that their gradients at time $t=0$ is the same,

$\cfrac{d\, F}{d\,t}= \omega=2\pi f$

which gives us the frequency, $f$  And so the associated period, $T$ is,

 $T=\cfrac{1}{f}={2\pi}\cfrac{d\, t}{d\,F}$

And the initial delay before the object start to response to the force is,

 $d=\cfrac{T}{8}=\cfrac{\pi}{4}\cfrac{d\, t}{d\,F}$.

This delayed response was at one time called "inertia", but later was decided that it does not exist.