There are several simulators around, mostly for trebuchets.
Atreb and Fat Sim
Atreb is considered to be the most accurate trebuchet simulator, and is a very powerful tool. It does have a limited demo, but it is very limited. Fat Sim is basically the same thing for Floating Arm Trebuchets. They are both Windows only.
TrebStar has both Mac and Windows versions. It is very easy to use, and the demo is quite functional. It can simulate basic Hinged Counterweight Trebuchets, though it can be forced to simulate Fixed Counterweight Trebuchets. It does not include friction so it will always overestimate range, but is great for optimizing dimensions. The free demo is very functional with only a few features disabled.
One of the more general purpose ones is Working Model. It has a free demo that does not allow saving, and is quite expensive. The demo can be useful, and was used by Chris G when he invented the King Arthur. It can handle pretty much any design, but is much harder to use. There is a somewhat recent Windows version, and a really old Mac version.
Phun is a completely free general purpose physics simulator (like working model). It is easy to use, and very modern, however it is harder to make things like slings and timed releases in Phun than working model. It supports Mac, Windows and Linux operating systems. Below is a video of a FAKA made with Phun: