The motion repeats itself in a regular fashion. The position of the mass is a function of the sine of the time.Ī second obvious characteristic of the graph may be its periodic nature. And the same can be said of a pendulum vibrating about a fixed position or of a guitar string or of the air inside of a wind instrument. There is something sinusoidal about the vibration of a mass on a spring. So the mass is vibrating back and forth about this fixed resting position over the course of time. A position of about 0.60 m cm above the detector represents the resting position of the mass. The vertical axis of the above graph represents the position of the mass relative to the motion detector. If y = sine(x) is plotted on a graphing calculator, a graph with this same shape would be created. Many students recognize the shape of this graph from experiences in Mathematics class. One obvious characteristic of the graph has to do with its shape. If you've taken time to ponder these questions, the following discussion will likely be more meaningful. And take a moment to reflect about what quantities on the graph might be important in understanding the mathematical description of a mass on a spring. For discussion sake, several points have been labeled on the graph to assist in the follow-up discussion.īefore reading on, take a moment to reflect on the type of information that is conveyed by the graph. And suppose that the data from the motion detector could represent the motion of the mass by a position vs. Suppose that a motion detector was placed below a vibrating mass on a spring in order to detect the changes in the mass's position over the course of time. It is a public domain acquired from WikiMedia Commons. (Special thanks to Oleg Alexandrov for the animation of the mass on a spring. Most objects that vibrate do so in a regular and repeated fashion their vibrations are periodic. In Physics, a motion that is regular and repeating is referred to as a periodic motion.
It's so predictable that you could set your watch by it. If it takes the mass 3.2 seconds for the mass to complete the first back and forth cycle, then it will take 3.2 seconds to complete the seventh back and forth cycle.
The time it takes to complete one back and forth cycle is always the same amount of time. The mass on the spring not only repeats the same motion, it does so in a regular fashion. If it were not for damping, the vibrations would endure forever (or at least until someone catches the mass and brings it to rest). Its motion repeats itself over and over again. Like the mass on a spring in the animation at the right, a vibrating object is moving over the same path over the course of time. A vibrating object is wiggling about a fixed position.
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