But if z is very small this distance, then A w p can be assumed to be constant over that,
this is exactly what we keep on doing in our parallel (( )) calculation, you know TPCTPI
calculation and remember, the entire theory of this equation of motion that we got is on
the assumption of linearity, which means that we have already said that all the
displacements are small in comparison to the body dimension, which means this part is
small compared to the draft. So, it is very logical to assume it is constant. In such a case,
my restoring force F s is this, but F s I I am writing as c z into z. First of all, you notice
that this is actually proportional to z if I of course, assume A w p is constant. So,
restoring force F s becomes proportional to the displacement and the constant of
proportionality is rho g A w p, which is my c z. So, I end up getting here that c z equal to
rho g A w p.