For completeness we compare both methods.
The method based on conservation of energy resulted in:
 |
(28) |
We note that this equation applies to all values of
. Therefore we can rewrite it as a function of
:
 |
(29) |
Solving the equation of motion resulted in:
 |
(30) |
Integrate
:
 |
(31) |
Substitute
into equation 30:
Which results in equation 31.