GO Electrical
0 votes

The following discrete-time equations result from the numerical integration of the differential equations of an un-damped simple harmonic oscillator with state variables $x$ and $y$. The integration time step is $h$.

$\frac{x_{k+1}-x_{k}}{h}=y_{k}$

$\frac{y_{k+1}-y_{k}}{h}=-x_{k}$

For this discrete-time system, which one of the following statements is TRUE?

  1. The system is not stable for $h > 0$
  2. The system is stable for $h > \frac{1}{\pi}$
  3. The system is stable for $0 < h <\frac{1}{2\pi}$
  4. The system is stable for $\frac{1}{2\pi}<h<\frac{1}{\pi}$
in new by (9.2k points)
recategorized by

Please log in or register to answer this question.

Answer:
Welcome to GATE Overflow, Electrical, where you can ask questions and receive answers from other members of the community.

847 questions
37 answers
10 comments
26,081 users