In this paper, a theory is developed that relates the natural response of an electric power system to sudden outages of transmission elements. The key development is in determining, via state-space analysis, the anticipated spectral content of either frequency or phase angle measurements as observed immediately following the sudden outage. This theoretical development mainly focuses on frequency measurements and the elements subjected to sudden outages are generators. For any sudden generator outage, the power system exhibits a very specific natural response in terms of its kinetic and potential energies. Kinetic energy in the system is directly related to each specific generator's rotational speed. It is shown that the effect can be seen directly in bus frequency measurements. Each remaining generator on the system has its own unique response to the sudden outage which contributes to the overall system natural response. This overall response is generally composed of oscillatory components which have specific frequencies. These oscillations, as measured by frequency meters, can be used to identify sudden element outages via their spectral content.