I designed this catapult so that it can be 100% 3d printed even in PLA (which is what I used). You can easily scale the springs and lever up or down for a perfect fit onto the frame. This catapult can shoot up to 20 feet. You can adjust the spring tension by rotating the springs by 90 degress on the pegs.
The frame will require a small amount of support, so make sure to enable support in your slicer. The picture shown includes the logo 'Series 1' as that is the type of printer I printed it with, but I removed that logo from the STL file for a cleaner look.
You can see a video of it in action here: