Roles and limitations of two widely publicized equations in predicting phase shift impulse response of a simple 2-D oscillator

This paper analyses a simple but analytically solvable 2-dimensional oscillator's phase shift impulse response to an external impulse noise. From the analysis, it is found that the initial state of the response is determined by the orthogonal projection-based formula by Hajimiri and Lee, and the final state is decided by the stochastic differential equation by Demir and co-workers. This work, however, shows that neither of the two equations can account for the transient behavior of the response.