1. Simple Harmonic Motion (SHM) What should I know About This Stuff?

2. Definition  Simple Harmonic Motion occurs when an event happens again and again and again with (relatively) the same amount of time between occurrences.  Examples:  Temperatures  Precipitation  Phases of the Moon  Light and Sound Waves  Electrical Currents  Etc.

3. We gotta have an equation!  The equation for simple harmonic motion is:

4. Things to know:  The period of oscillation is the time it takes to complete one full cycle.  The vertical shift of the equilibrium is also the average value of the function through any number of complete oscillations.  Your calculator does a sinusoidal regression, so we normally use the sine for the equation.  It is more convenient to use the cosine when an object begins oscillating at either a maximum or a minimum point in its motion (ie. A mass bobbing up and down on a spring).

5. Period  The period is the time it takes to go through one oscillation.  Notice how the period does not depend on the amplitude. Hmmmm….

6. Example:  Given the following equation, determine the length of time required to complete one oscillation.

7. Phase Shift  The phase shift is the left-to-right movement of a sinusoidal curve.  Mathematicians and physicists differ in their opinion on this matter.  Physicist’s view: You can center your axes wherever you want. This would eliminate the need for a vertical or horizontal shift.  Mathematician’s view: You need the axes properly located to account for the real-life scenario that’s happening.  At any rate, the phase-shift is given by:

8. Phase Shift (example):

9. Vertical Jump and Average Value  Temperature is very periodic.  Therefore, if we were to perform a sine regression on a set of temperatures, we could get a sine curve that represents the data.

10. Vertical Jump and Average Value

11. The average value of this sine function (for now) is 57.17. What is the period?

12. Example