History– A trebuchet, also sometimes called a trebucket is a medieval siege engine, a weapon employed either to batter masonry or to throw projectiles over walls. The trebuchet is thought to have been invented in China between the 5th and 3rd centuries BC. The device reached Europe around 500 AD.
How it works – A trebuchet is powered by a falling counterweight acting through a beam acting as a lever. The trebuchet is cocked by raising the counterweight(1). A trigger mechanism holds the counterweight up. The sling is arranged horizontally in a trough parallel to the beam, toward the counterweight, and the projectile placed in its pouch. When the trigger is released, the counterweight falls and the beam pulls the sling, at first horizontally along the trough in the base of the frame(2). Soon after, the sling lifts off and whips in an arc upwards(3). When the projectile moves close to the point where the taut sling makes about a 45° angle with the horizontal(4), the free end of the sling slips from the hook, and the missile flies free toward its target(5).
Equations to consider Force F=ma
Potential Energy PE=mgh
Kinetic Energy KE=1/2mv^2
Machine Elements and Mechanical Design 4th edition