The document provides information on vibrations including definitions of key terms like natural frequency, forced vibrations, and damped vibrations. It also discusses single degree of freedom systems and how to calculate the natural frequency of longitudinal and transverse vibrations in beams and shafts using different methods. An example is provided to show how to calculate the natural frequencies of longitudinal and transverse vibrations for a cantilever shaft with a mass at the free end. Formulas are given for stiffness, static deflection, and natural frequency of beams and shafts.