(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Determine the stability property of the following equibrilium solution:

(0,0) of

[tex] \ddot{x}+ \alpha x +x=0 [/tex] with [tex] \alpha \in \mathbb{R} [/tex]

2. Relevant equations

- A solution isLyapunov stableif for each [itex] \epsilon[/itex] there is a [itex] \delta [/itex] such that: [tex]||x(0)|| \leq \delta[/tex] yields [tex]||x(t)|| \leq \epsilon [/tex]

- A solution isunstableif it isn't stable.

- A solution isasymptotically stableif there is a delta such that: [tex] ||x(0)|| \leq \delta [/tex] yields [tex] \lim_{t \rightarrow \infty} ||x(t)|| = 0[/tex]

Note: x can be a vector.

3. The attempt at a solution

I don't know how to use these defintions. Can I just use the 2-norm? Can someone explain me how this works?

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Stability equibrilium solution

Can you offer guidance or do you also need help?

Draft saved
Draft deleted

**Physics Forums | Science Articles, Homework Help, Discussion**