All I really need is the length the spring is pulled back from equilibrium, the weight of the projectile, the distance it could fire at a certain angle. If people could find the spring factor that'd be great too, but I can solve for it I believe.
On the off chance that you can come up with numbers on your own, you could check out Vitruvius' descriptions on how to build a ballista (section 1-9). He was an ancient Roman author who can prove quite helpful for us when it comes to Roman building techniques. This is about as close you get with historical writings, otherwise you'll probably have to find a modern reconstruction plan (perhaps from a museum), but I'm afraid I can't recall having read about any such reconstructions.