A causal block diagram representation of a spring mass damper system.
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A causal block diagram representation of a spring mass damper system. Simulated using a causal block simulator.
The formula we follow to achieve this is: 0 = 100 - 2y' - 100y - y".
Here, the friction coefficient is 0.02 Ns/m and the spring constant is 1 N/m with the block weighing in at 0.01 kg.
The simulated position (distance) of the spring is described by the following graph.
In the example we are interested in the spring constant k which results in almost zero oscillation (equilibrium) in the time frame of [5, 7] seconds after impulse release.