If you're seeing this message, it means we're having trouble loading external resources on our website.

If you're behind a web filter, please make sure that the domains *.kastatic.org and *.kasandbox.org are unblocked.

## Integrated math 3

### Course: Integrated math 3>Unit 9

Lesson 2: Interpreting features of functions

# Periodicity of algebraic models

Sal analyzes the periodicity of graphs that model real world situations.

## Want to join the conversation?

• It has occurred to me that the sine could be defined in terms of periodic motion of a spring, where F = -kx is proportional to the negative of the displacement, and results in a periodic displacement function. I suspect that it has been proven at some point in the past that this is the same function as the sine (the y coordinate) in the unit circle, since this is how we calculate the displacement of an oscillating spring + weight. However, how do we know they are the same? What is the proof of this?
Intuitively it seems that there is a simple relationship between these two kinds of motion, circular and oscillating.

With gravity, acceleration is constant, velocity is a linear function v = at + s, and distance is quadratic.
With an oscillating spring, acceleration is a linear function of and in the opposite direction of displacement. But the displacement itself oscillates, so the acceleration also oscillates. Then so does the velocity. I imagine all 3 of these are sine functions.
Is there an exponential function (with a common factor of displacement, or something) somehow involved in this?