Can someone check my logic? simple harmonic motion.

[aliciagu]

Homework Statement

Is the daily movement of a student from home to school and back simple harmonic motion?

Homework Equations

The Attempt at a Solution

I don't think it is. This type of movement is linear. It involves distance, speed and so on. It does not follow a sinusoidal wave pattern, either because though it is periodic, it's not regular. Does that make sense? Can someone else perhaps explain it better?

 

[G01]

Simple Harmonic motion is defind by the following differential equation:

$$m/frac{d^2x}{dt^2}=-kx$$

The solution to this equation is a sinusoidal function. As you said, the motion of the student is periodic, but not sinusoidal.

I agree with you. The student's motion corresponds to a square wave (graph his displacement vs. time) This is not simple harmonic motion, but instead falls into the realm of complex harmonic motion.