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I'm working with a simulator(Box2D) and need to create these conditions.

I have a perpetual seesaw with two objects on either side. I'd like for the following conditions to be met.

The first object will be on the seesaw and the second object will be dropped from a height. This will launch the first object and vice versa.

  1. When their masses are the same, and the first object is dropped from a height, the second object should be launched to the same height.
  2. If a heavier object is dropped from a height, the lighter object has to be launched higher
  3. If a lighter object is dropped from a height, the heavier object has to be launched lower.

Under what conditions would this work?

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Presumably you know that perpetual motion machines don't exist :-), but for a simulator we'll allow frictionless bearings, a massless lever for the seesaw, etc. In this situation, all you need to do is calculate the kinetic energy of the first dropped object, transfer all that kinetic energy to the other object, and then calculate the height to which the second object will fly. Use the standard equations, e.g. $v = a*t$ , $KE = \frac{m*v^2}{2}$ , $s= v_0*t + \frac{a*t^2}{2}$ , to get the values of interest.

Note that if you have an asymmetric seesaw, you'll have to work in the appropriate lever force ratio as well.

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I think that you will not reach it. I don't have experience with Box2D, but such simulators usually have some damping (which usually can be set to zero, but that can lead to bad results).

Assuming you can set damping to zero, so your simulation will try to keep all energy, you will run into another problem: inacuraccy. This will add or remove energy by small ammounts, but it will accumulate over time, so you will not reach PERPETUALY repeating motion (and whether it will stop or start bouncing higher than it should is chaotic). But it can be good enough for your purposes. I guess that you are not dealing with nonuniform gravity, which can wreak havoc in simply coded simulation, so i guess it will not noticably change before most people get bored watching bouncing boxes.

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