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V (x, x) = m² + 1/kx²

V (x, x) = m² + 1/kx²

Elements Of Electromagnetics
Elements Of Electromagnetics
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
ChapterMA: Math Assessment
Section: Chapter Questions
Problem 1.1MA
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If you have a spring mass damper system, given by m*x_double_dot + c*x_dot + kx = 0 where m, c, k (all positive scalars) are the mass, damper coefficient, and spring coefficient, respectively. x ∈ R represents the displacement of the mass.

Let us then discuss the stability of the system by using Lyapunov stability theorem. Consider the system energy as a candidate Lyapunov function shown in the image. 

Discuss the positive definiteness of V (x, x_dot).

Derive the Lyapunov rate of this system (i.e., V_dot ), and discuss the stability property of the
system based on the information we gain from ̇V_dot .

V (x, x) = m² + 1/kx²
Transcribed Image Text:V (x, x) = m² + 1/kx²
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