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SystemTheory

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This produces exponential motion. My problem in building an educational simulator is this, I want to compute the time down the ramp of length xL rather than make educated guesses in the simulator time setting.

I've tried solving for time in the DE, with no result. I've also tried to apply Conservation of Energy but I'm still struggling with an answer. Anyone recognize a solution to this apparently simple challenge?

I've posed the problem in this thread:

https://www.physicsforums.com/showthread.php?t=357732