Linear and nonlinear spring. Free oscillations with one degree-of-freedom of motion. Equivalent rigidity. Kinetic and potential energy of the one degree-of-freedom system. Lagrange equations for motion of the one degree-of-freedom system. Riley`s procedure for determining circular frequencies. Curled and transversal oscillations of massive girders. Free oscillations with viscous friction force and sliding force in the one degree-of-freedom system. Forced oscillations in the one-degree-of-freedom system. Forced oscillations under Dirak and Heaviside forces. Kinetic and potential energy of the two degree-of-freedom system. Lagrange motion equations for the two degree system. Integration of the motion equation of the two degree-of-freedom system. Forced oscillations of the two degree-of-freedom system. Resonance. Dynamic buffer. Influence of viscous friction on small oscillations in the two degree-of-freedom system. Definition on the stability of motion. Transversal oscillations of a string. Longitudinal oscillations of a beam. Curled oscillations of a beam. Transversal oscillations of a beam. Critical speeds of elastic shafts. Laval`s paradox.