Transients in Simple Undamped Oscillators Under Inertial Disturbances

Single-degree-of-freedom systems acted upon inertial forces are often found in technical applications. In this paper we shall study the transients in the vibrations of the system due to a change in speed in the machine in which the inertial forces are generated. We shall state the problem in the most general case, and then study the starting and the stopping with constant acceleration. After giving the exact solution of the problem we shall derive very simple approximate formulas for the determination of the maximum amplitude reached in these transients.