EXAMPLE 2: POTENTIAL ENERGY

Calculate
the potential energy of the spring force. Assume the spring has a free length
of _{}.
Solution for
2D motion

In
polar coordinates
_{}
Therefore,
_{}
Integrating
(2) gives
_{}
Substituting
(3) into (4) gives
_{}
Integration
using _{} so that _{} gives
_{}
Therefore,
the potential energy for the spring force is
_{}