This chapter discusses one-dimensional vibrations in a simple mechanical system consisting of a mass, a spring and a damping element. Since the vibrations can be fully described in one dimension, this is also called a system with one degree of freedom. First, the use of complex notation is shown for harmonic vibrations as a basis for later applications in acoustic vibrations and sound fields. Next, the vibrations in a resonant mechanical system are dealt with, as a basis for numerous applications in resonant acoustic systems. Finally, the theory for vibration isolation is explained as this has fundamental importance for noise control of machines and equipment in practice. The description follows the terminology and concepts in ISO 2041. The human body can sense vibrations in the frequency range from 1 Hz to 80 Hz. The sensitivity depends on the direction of vibration relative to the body.