Looking for some pointers on how to approach this problem:(adsbygoogle = window.adsbygoogle || []).push({});

I'm considering a system like the following - two springs and two masses connected in sequence:

http://www.myphysicslab.com/dbl_spring1.html

I would like to find the following:

Given m1, m2, k1, k2. The springs are compressed each by a certain amount (x1start and x2start) and the velocities are set to 0. The springs can be released at any point in time. Once a spring is released and it stretches so that its stretch reaches a peak, it is clamped at that position. Once both springs reach their peak stretch the simulation is ended. Here is what I'm trying to find:

Assuming the left spring is released at t=0. At what time should the right spring be released to maximize the peak velocity of the right block.

I could iterate numerically using Runge-Kutta and try stepping up the release time of the right spring and record peak velocity of the right block but that seems very brute forced. I would like to find a better solution for this if possible.

As a side question, I was wondering if there was an analytical solution to this system?

Thanks for any pointers.

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# Double Spring Mass System - Maximizing Velocity

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