# Equation for force needed to replace energy lost by a pendulum each swing

I'm sure this is just a question of not knowing the right search terms, but I'm trying to find out how much energy I would need to put back into a pendulum in order to keep it swinging forever.

Specifically, I'm toying with the idea of building something like one of those automatic swings that rocks a baby but mechanical, rather than electric and possibly large enough for a bigger kid or even an adult. Kind of like a giant grandfather clock with a human pendulum.

I'm sure the amount of push required to keep the swing going indefinitely would be in proportion to the weight of the pendulum (or kid, or lazy grown up) but while I've found dozens of websites with equations describing the period of the pendulum but nothing describing with how much force I need to push to keep it going. Can someone direct me to a resource or suggest different search terms?

• I would think it would depend on how it's weighted. Maybe more design details would be helpful.
– user234190
Jul 5, 2019 at 23:16
• I don't really have any design ideas since I don't really know what I'm going to need. Once I know that, for example, to keep a 25kg child in motion I need to push with x Newtons of force, I can start deciding if I can push closer to the pivot or if I need to get closer to the weight, etc. I'm going to design it around the requirements since I don't expect the requirements to be as cooperative to change as the design will be. Jul 5, 2019 at 23:20
• Interestingly I've actually put together a circuit whose main job is to keep a pendulum swinging in my local science museum. Our way of doing it was to have a circuit drive a cylindrical magnet temporarily when a metallic cuff on the cable supporting the pendulum entered the gap between the magnets. This would pull the cable while the magnet is on, putting energy back into the system. I had to calculate the timing so I could set the delay. It is based on the one used in my physics dept. Jul 6, 2019 at 0:13
• So you did need the period of the pendulum for the timing, but how did you know how much force to apply? Jul 6, 2019 at 4:05