GATE Electrical Engineering (EE) 2015 Shift 2 Solved Paper

The following discrete-time equations result from the numerical integration of the differential equations of an un-damped simple harmonic oscillator with state variables $\mathrm{x}$ and $\mathrm{y}$. the integration time step is $\mathrm{h}$.
$\frac{{\mathit{x}}_{\mathit{k}+1}-{\mathit{x}}_{\mathit{k}}}{\mathit{h}}={\mathit{y}}_{\mathit{k}}$
$\frac{{\mathit{y}}_{\mathit{k}+1}-{\mathit{y}}_{\mathit{k}}}{\mathit{h}}=-{\mathit{x}}_{\mathit{k}}$
For this discrete-time system, which one of the following statements is TRUE?