  In this work, the normal modes of a two-dimensional oscillating system have
been studied from a theoretical and experimental point of view. The normal
frequencies predicted by the Hessian matrix for a coupled two-dimensional
particle system are compared to those obtained for a real system consisting of
two oscillating smartphones coupled one to the other by springs. Experiments
are performed on an air table in order to remove the friction forces. The
oscillation data are captured by the acceleration sensor of the smartphones and
exported to file for further analysis. The experimental frequencies compare
reasonably well with the theoretical predictions, namely, within 1.7 % of
discrepancy.
