From the course: Assembling Calculus
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Simple harmonic motion
From the course: Assembling Calculus
Simple harmonic motion
- [Instructor] In this movie, we'll talk about real world systems that vary over time in a way that we can model as sine or cosine waves. This type of behavior is called simple harmonic motion, and it comes from the relationship between a sine or cosine wave and its second derivative. A mass bobbing on a spring or a pendulum swinging back and forth are both examples of simple harmonic motion. Let's see where the math comes from for the example of a mass on a spring. Newton came up with a relationship that the force on an object equals its mass times its acceleration. This is usually written F equals ma, where the force and acceleration in this case will be functions of time. The acceleration is the second derivative of position of an object, as we learned earlier, so we can write it that way too. How can we figure out though what forces are being exerted on our mass and spring and how can we write them down as equations?…
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