Trying to understand how to model the natural movements of a pendulum in a programming language.

 

Not sure where to start, I know that certain constants must be involved but unsure exactly how this would all work together.

 

If I apply a certain amount of force with a certain length of string I should tend to get certain amounts of arc, swing, circular rotation and duration of momentum in relation to the original force and gravity.

 

So somehow math values such as pi (for circular motion), a gravitational constant, possible phi or theta, ranging variables for string length and forces applied, etc.... must all work together. Perhaps "e" would be involved somehow as well....?

 

I'd like the programming routine to be very close to a real world example, as far as accuracy goes.

 

In other words if i take a string length of 8 inches, with say a one ounce weight, and apply a specifc amount of force, it will swing X times in a linear fashion, losing Y amount of momentum, at the occurence of duration XY it will stop swinging in a linear fashion and begin Clockwise rotation and do so XXY times, again losing Y amount of momentum and then after another duration move counter clock wise, etc.... but...

 

Id like the software to predict very closely what would actually happen in the real world scenario.

 

How would formula being written to solve this scenario?

 

Math examples?  Code examples?