Question:
Stable or unstable system
Please show steps to evaluate for correct answer.
1. Systems are unstable if their characteristic equations have a positive root (solution). Determine whether each of the following characteristic equations represents a stable or unstable system.
(i) s3 + 6 s2 + 11s + 6 = 0
(ii) s3 + s2 - 8s - 12 = 0
2) In a Hooke's law experiment, equal increments of force, w, are applied to a metal rod and the length of the rod is recorded. Within the elastic limit, the increases of length, x, are found to be equal.
After the application of the 10th increment of force, the length of the rod is found to be 50.03 mm and after the 15th increment of force the rod's length is found to be 50.08 mm. Determine the original length of the rod, l, and evaluate
Σ10n=1(l+nx)