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Simple harmonic motion time!

We are getting ahead of the class even more, however, we now have problems on simple harmonic motion. My favorite topic in intro mechanics; though we don't do it as throughly as we do in Physics 262, the more advanced mechanics class for majors.

Let's start off with a couple simple problems:

First, how do we calculate period and frequency.

Second, when do we get cosine vs sin functions for simple harmonic motion.

Then some more demanding problems.

A more general phase angle problem; so we don't just have a plain sin or cosine function.

What are some possible solutions to our second-order differential equation for simple harmonic motion? Remember a nice thing about differential equations is that it doesn't matter how we get our answer because we can always check our answer.

Then last, but not least, given a specific harmonic oscillator, how do we find its velocity and acceleration at particular times.