Frequency and Period - Questions 8 Help

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Vibrating objects undergo back-and-forth vibrations about a fixed location. Two physical quantities that describe these vibrations are frequency and period. While related, they have quite different definitions, meanings, and mathematics.

There are two similar versions of this question. Here is one of those versions:

Version 1:

A mass on a spring is undergoing vibrations. A computer-interfaced motion detector placed below the mass detects its position as a function of time. Consider the two cases below. In which case does the mass have the greatest period?

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.

Try this link to The Physics Classroom Tutorial for more help with the concepts of frequency and period:

Frequency and Period