Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. Join them; it only takes a minute:

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top
  1. Study whether the null solution of the system: $$\begin{cases} \frac{dx_1}{dt}=x_2(t)\\ \frac{dx_2}{dt}=-w(t)^2 x_1(t)\\ \end{cases} $$ is Lyapunov stable, where $$ w(t)= \begin{cases} 0.4 & \text{for } 2k\pi \leq t < (2k + 1)\pi\\ 0.6 & \text{for } (2k-1)\pi \leq t < 2k\pi \end{cases} $$
  2. Carry out the stability analysis of $$\frac{d^2x(t)}{dt^2}+1-\cos(x(t))=0$$
share|cite|improve this question
I tried to solve the problem 1 by solve it recursively. but it turned out to be quit complicate. And, to the No.2 I've found a solution now. Thank you for your attention. – BerSerK Oct 15 '11 at 11:50

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Browse other questions tagged or ask your own question.