The period of a vibrating object refers to the amount of time it takes the object to complete one cycle. Because it is a time, it is expressed in units such as seconds or minutes. To determine the period, similar measurements can be made as discussed in the previous paragraph - the number of complete vibrational cycles in a given amount of time. The calculation of period from such data involves dividing the time by the number of cycles. As you can see, the unit would be a time unit per cycles or simply the time unit.
The plot shows time plotted along the horizontal axis. And the familiar sinusoidal, up-and-down repeating changes are shown. You can start at a high point on the sinusoidal curve and trace along the curve to the next highest point. This is referred to as a cycle. The case with the greatest period is the one that completes this cycle in the greatest amount of time. That is to say, the high points on the graph are spaced furthest apart.