Here are some links I’ve found that have information on building small catapults.
Please note: some of these designs require materials we don’t have or will take too long to build.
Here is a page on this site that breaks down the catapult design process.
Click here for a page on this site with directions for a catapult made from office supplies.
This site has lots of background information, but I can’t verify the source
of the content on the site.
This person does not appear to be an expert but the site is still interesting.
Apparently he is an actor who portrays a medieval knight.