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Period and Frequency of a Mass on a Spring - help8

Not every mass/spring system is the same. Some have strong springs (large k) and others weak springs (smaller k). Some have a massive object attached to the spring and others have a less massive object. How do these variables affect the period and the frequency of a vibrating mass on a spring? That's the basic idea of this activity. Learn more about it in the How to Think About This Situation section.

There are four similar versions of this question. Here is one of the versions:

Version 1:

Anna Litical is experimenting with an object vibrating up and down on the end of a spring. She is studying the effect of object mass (m), spring constant (k), and spring length (L) upon the period. The parameter values used for three trials are shown. Rank the three trials in order of their period (T).

The Relationship
Perhaps you have done the experiment. It certainly is more exciting to discover the relationship on your own than to be told what it is. And if you have done the experiment, then you know that the two variables that affect the period of a vibrating mass on a spring are the mass of the object and the spring constant of the spring. A more massive object hung on the spring will vibrate with a longer period and a smaller frequency. Mass and period are directly related while mass and frequency are inversely related. And a stronger (stiffer) spring with a larger spring constant results in a shorter period and a higher frequency. That is, an object on a stiff spring will take less time to vibrate back and forth; the frequency at which it does its vibrations will be higher than it would be for a weaker (less rigid) spring. Spring constant and period are inversely related while spring constant and frequency are directly related.

The formula for determining the period includes m/k as a ratio in the equation. In fact, the period (T) of a mass/spring system is directly proportional to the square root of the m/k ratio of the mass/spring system. The proportionality statement is ...

T ∝ √(m/k)

Analyze It
Given the above relationship, your task is to analyze the provided data. Give attention to the mass (m) and the spring constant (k). Disregard the spring length as it has nothing to do with the question. Isolate the relevant variable that is being changed from trial to trial and take your time at ranking the trials. You got this!

Try this link to The Physics Classroom Tutorial for more help with the motion of a vibrating mass on a spring:

Motion of a Mass on a Spring