(Newton's seonc law of motion)
(forces are additive and these are the only ones in this situation)
(gravity is a constant downward pull)
is such that the distance between pivot and bob is constant
(air and pivot resistance)
(action on the pivot)
Consider the position of the bob as a function of .
By assumptions 1 and 2:
In the direction of motion
As a system,
Choose units so that :
To obtain a numerical solution, the parameters, initial conditions, and the time domain must be specified numerically. In the following, I use for and for .
Start with an unforced and no drag situation, and consider different initial conditions and .
What is the period?
Now add some forcing at a period near the natural period.