\(-\cfrac { d^{ 2 }x }{ dt^{ 2 } }=\cfrac { 1 }{ m } \psi _{ c } +{ \cfrac { u }{ \psi _{ c }+u } }\cfrac { 1 }{ e^{ u }\left( { e^{ 2u }-1 } \right) ^{ 1/2 } } (\cfrac { dx }{ dt } )^{ 2 }\)
which shows that the dominant effect of,
\(\cfrac { 1 }{ e^{ u }\left( { e^{ 2u }-1 } \right) ^{ 1/2 }} =\cfrac{1}{cosh(x-\cfrac{x_a}{2})sinh(x-\cfrac{x_a}{2})}=\cfrac{2}{sinh(2x-x_a)}=2csch(2x-x_a)\)
in the expression.
