We consider a mass-spring-damper system with force (N) as input and displacement

Question

We consider a mass-spring-damper system with force (N) as input and displacement (m) as output, which is effectively a second-order system without zeros. The plot below is the step response of the system under step input with amplitude of 5N. Find the static gain of the system. Find the damping ratio based on OS%. Find the undamped natural frequency of the system with the plot. If the first-principle modeling of the system leads to the following transfer function: G(s) = 1/Ms^2 + bs + K, where M, b and K are mass, damping coefficient and stiffness, respectively. Find out the values of M, b and K based on your results in 1), 2) and 3).

Explanation / Answer

The answer of following question is as follows.

The static gain is 7 .

The value of maximum damping ratio is 78 .

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