Begin by taping your cylinder to the middle of your popsicle stick. Simply lay a piece of tape over the cylinder and in the same direction as the popsicle stick so the tape cannot be seen from the opposite side.
Flip the popsicle stick over. On one end you are going to attach a plastic cap. Place a bit of tape or glue on one end of the stick and firmly hold the cap until dry.
And that's it! There's the general idea for your catapult.