Imagine a standard pendulum. I understand how to work the physics on one but what if you attached that pendulum to a pulley at the top and could apply tension through the line? Let's say you released it at 45 degrees then some degrees later you applied some amount of tension through the pulley forcing the pendulum to both deviate from a circular path and increase in velocity. How could I come up with a function that showed where the pendulum would be with some tension applied and let go at some angle? The radius and weight of the pendulum would be fixed. Thanks for your time. I was thinking you could launch people even farther if you used this for a rope swing. They would swing then at some angle a tension would be applied and they would follow a more parabolic path and get launched. Also, this is not a homework question please don't move it! I've been out of physics for a long time and was just looking for help in designing a new rope swing. I have my college physics book and am reading the crap out of it so please no negative comments.