One of the most common and important types of motion is oscillatory motion—a repetitive motion back and forth around an equilibrium position. Swinging chandeliers, vibrating guitar strings, the electrons in cell phone circuits, and even atoms in solids are all undergoing oscillatory motion. In addition, oscillations are the sources of waves, our subject in the following two chapters. Oscillations play a major role in all fields of science and engineering.

FIGURE 15.1 shows position-versus-time graphs for two different oscillating systems. The shape of the graph depends on the details of the oscillator, but all oscillators have two things in common:

1. The oscillations take place around an equilibrium position.

2. The motion is periodic, repeating at regular intervals of time.

FIGURE 15.1 Examples of oscillatory motion.

Full Alternative Text

The time to complete one full cycle, or one oscillation, is called the period of the oscillation. Period is represented by the symbol T.

A system can oscillate in many ways, but the most fundamental oscillation is the smooth sinusoidal oscillation (i.e., like a sine or cosine) of Figure 15.1. This sinusoidal oscillation is called simple harmonic motion, abbreviated SHM. You’ll learn in more advanced courses that any oscillation can be represented as a sum of sinusoidal oscillations, so SHM is the basis for understanding all oscillatory motion.

The prototype of simple harmonic motion is a mass oscillating on a spring. FIGURE 15.2 shows an air-track glider attached to a spring. If the glider is pulled out a few centimeters and released, it oscillates back and forth. The graph shows an actual air-track measurement in which the glider’s position was recorded 20 times per second. This is a position-versus-time graph that has been rotated 90° from its usual orientation to match the motion of the glider. You can see that it’s a sinusoidal oscillation—simple harmonic motion.

FIGURE 15.2 A prototype simple-harmonic-motion experiment.

As Figures 15.1 and 15.2 show, an oscillator moves back and forth between $x=-A$ and $x=+A$, where A, the amplitude of the motion, is the maximum displacement from equilibrium. Notice that the amplitude is the distance from the axis to a maximum or minimum, not the distance from the minimum to the maximum.

Period and amplitude are two important characteristics of oscillatory motion. A third is the frequency, f, which is the number of cycles or oscillations completed per second. If one cycle takes T seconds, the oscillator can complete $1/T$ cycles each second. That is, period and frequency are inverses of each other:

The units of frequency are hertz, abbreviated Hz, named in honor of the German physicist Heinrich Hertz, who produced the first artificially generated radio waves in 1887. By definition,

We will often deal with very rapid oscillations and make use of the units shown in TABLE 15.1. For example, electrons oscillating back and forth at 101 MHz in an FM radio circuit have period $T=1/(101\times {10}^6\text{Hz})=9.9\times {10}^{-9}\text{s}=9.9\text{ns}$.