Suppose we have 2 springs with different values for m and k. The first spring is given an arbitrary dampening value, c, to slow it to a stop. How can we calculate c for the second spring such that both springs would both stop together?

I realise that mathematically the spring never truly stop and just keeps oscillating infinitely while the amplitude decreases. So I suppose the question is how you would determine a c value for the second spring that would cause its amplitude to converge with that of the first spring.

Force is calculated as follows:

F = (c * -v + -k * (pos - 100) + externalForce), where 100 equals the length of the string at rest. Starting position is 100 and a constant external force is applied in random intervals for a random number of timesteps. Otherwise, externalForce = 0, and the spring slows to a stop. It should be noted that the externalForce may be applied while the spring is still in motion.

  • \$\begingroup\$ Be sure to include the formula that includes c in your definition, and the initial momentum and displacement of each spring \$\endgroup\$
    – DMGregory
    Mar 10, 2023 at 2:45
  • \$\begingroup\$ @DMGregory, changes made. \$\endgroup\$
    – 19172281
    Mar 10, 2023 at 3:03
  • \$\begingroup\$ Now you'll need to define external force and how it varies over its period (of what?). \$\endgroup\$
    – DMGregory
    Mar 10, 2023 at 3:39
  • \$\begingroup\$ @DMGregory, I hope that clarifies things :) \$\endgroup\$
    – 19172281
    Mar 10, 2023 at 3:47
  • 1
    \$\begingroup\$ I’m voting to close this question because it is a Physics question, not a GameDev. \$\endgroup\$
    – Kromster
    Mar 10, 2023 at 10:10


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