In this work we will model the dynamics of the simple harmonic oscillator using discrete variables. The resulting recurrence relations were written as matrix transformations and, from a diagonalization process, we will show that the solution obtained converges to the well-known analytical solutions of the system. This approach avoids the continuity hypothesis and is relevant as it describes the dynamical of this particular system from a computational point of view. Furthermore, the algorithm we are proposing was implemented, and an error analysis was built from the principle of the conservation of mechanical energy.
Keywords:
Discretization; Simulation; harmonic oscillator
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