Chapter 6.4, Problem 35PE

The brightness of a "young" star sometimes increases and decreases as a result of regional areas of "hot" and "cold" on the star's surface as well as variations in the density of the star's planet-forming debris, which can obstruct light Suppose that for a particular star, the average magnitude (measure of brightness) is $4.3$ with a variation of $\pm 0.31$ (on the magnitude scale, brighter objects have a smaller magnitude than dimmer objects). Furthermore, the magnitude of a star is initially observed to be $4.61$ , and the time between minimum brightness and maximum brightness is $6.4$ days. Write a simple harmonic motion model to describe the magnitude $M$ of the star for day $t$ .