Abstract
This chapter is dedicated to understanding and studying a didactic case represented by a free vibration of a linear oscillator with a single degree of freedom. Mathematical equations of the problem will be detailed as well as the solution that goes with single degree of freedom oscillator for translational vibration for all cases: free undamped oscillator, as well as free damped oscillator, and torsional free undamped vibration passing by critical, subcritical, and over damping system. At the end of the chapter, some examples will be treated.