Consider the following system of equations
Find the nature of the critical point ,0( of the corresponding linear system.
The given system of equations is: \[ \frac{d\mathbf{x}}{dt} = \mathbf{y} \] \[ \frac{d\mathbf{y}}{dt} = -\mathbf{k}^2 \sin \mathbf{x} \] ### Step 1: Finding the Critical Point The critical points are found by setting the derivatives to zero: \[ \mathbf{y} = 0, \quad -\mathbf{k}^2 \sin \mathbf{x} = 0 \] Since _______ ____ _______ ___ ______ ______ _________.
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Consider the following system of equations
Find the nature of the critical point ,0( of the corresponding linear system.