15.1 Simple harmonic motion

When you pluck a guitar string, the resulting sound has a steady tone and lasts a long time ( [link] ). The string vibrates around an equilibrium position, and one oscillation is completed when the string starts from the initial position, travels to one of the extreme positions, then to the other extreme position, and returns to its initial position. We define periodic motion    to be any motion that repeats itself at regular time intervals, such as exhibited by the guitar string or by a child swinging on a swing. In this section, we study the basic characteristics of oscillations and their mathematical description.

Period and frequency in oscillations

In the absence of friction, the time to complete one oscillation remains constant and is called the period ( T )    . Its units are usually seconds, but may be any convenient unit of time. The word ‘period’ refers to the time for some event whether repetitive or not, but in this chapter, we shall deal primarily in periodic motion, which is by definition repetitive.

A concept closely related to period is the frequency of an event. Frequency ( f ) is defined to be the number of events per unit time. For periodic motion, frequency is the number of oscillations per unit time. The relationship between frequency and period is

The SI unit for frequency is the hertz (Hz) and is defined as one cycle per second :

A cycle is one complete oscillation    .