Question

Suppose a certain variable star has a period of 10 days. The average brightness of the star is 3.6 magnitudes, and the maximum variation from the average is 0.3 magnitude. Assuming that the variation in brightness is simple harmonic, find an equation that gives the brightness of the star as a function of time. (Let y be the brightness in magnitudes and let t be the time in days. Suppose that when t

Answer 1

Answer: B(t) = (0.03*Cos( pi*t/5)  + 3.6) magnitudes.

Step-by-step explanation:

The question is not complete, but I will suppose that when t = 0, the brightness of the star is at the mean of 3.6 magnitudes.

Now, we know that the brightness oscillates with a period of 10 days and that the variation is equal to 0.3 magnitudes.

We know that the behavior is simple harmonic, so we can write this as:

B(t) = A*Cos(c*t) + K

Where A, c, and K are constants.

A defines the extreme values of the oscillation, so here we will have that A = 0.3 magnitudes.

K is the point around we have the oscillation, K is the average brightness of the star; K = 3.6 magnitudes.

c is a constant such the period is equal to 10 days.

We know that the period of the cosine function is equal to 2*pi

then we have: c*10 = 2pi

c = 2*pi/10 = pi/5

Then our equation is:

B(t) = (0.03*Cos( pi*t/5)  + 3.6) magnitudes.