# How to analysis the stability of these ODE?

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 $$\frac{d^2x(t)}{dt^2}+1-\cos(x(t))=0$$
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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