We illustrated the duration integral method for solving for motions when F = F(v), by doing the example F= -bv, of a boat slowed by water resistance.
We then began our third special case, when F=F(x). We defined
potential energy V, and discussed qualitative consequences of the
fact that a particle's potential energy must be less than its total
energy. Discussed allowed and forbidden regions for particles of fixed
energy, and bound states in potential wells (where motion is allowed
only between finite positions). Considered unbound particles. Did
example of gravitational escape, where the escape velocity gives just
enough kinetic energy for the particle to surmount the potential
barrier and escape to 
.
-- KB