Question

How does the period of an oscillation in a spring-mass system depend on mass and amplitude? How can I express this graphically for period as a function of mass, period as a function of the square root of the mass, and period as a function of amplitude?

Answer 1

OK, the period of oscillation, `T = 2pisqrt(m/k)` so it maybe easier to analyse if we square everything `T^2 = 4pi^2.(m/k)`

Explanation:

This means that `T^2 prop m` and also `T^2` is independent of the amplitude (providing we retain the experimental conditions that satisfy the assumptions underlying the model, e.g. `F prop x`)

Now the graphing;

T vs. m will thus give you a square root graph ...

Taken from: http://www.ltcconline.net/greenl/courses/103a/keys/exam2PracticeExam/key.htm

T vs. `sqrt(m)` will give a linear graph with a gradient equal to `(2pi)/sqrtk`

(Don’t think a graph is required here)

Finally, T vs. A will give a horizontal line (until the spring starts to jump, or overstretch etc.) showing no dependence.