The magnitude of a star named Delta Cuphea varies from an apparent magnitude of 3.6 to an apparent magnitude of 4.3 with a period of 5.4 days. At t = 0 days, the star is at its brightest with a magnitude of 3.6 (on the magnitude scale, brighter objects have a smaller magnitude than dimmer objects). Write a simple harmonic motion model to describe the magnitude M of the star for day t .
The magnitude of a star named Delta Cuphea varies from an apparent magnitude of 3.6 to an apparent magnitude of 4.3 with a period of 5.4 days. At t = 0 days, the star is at its brightest with a magnitude of 3.6 (on the magnitude scale, brighter objects have a smaller magnitude than dimmer objects). Write a simple harmonic motion model to describe the magnitude M of the star for day t .
Solution Summary: The author describes the simple harmonic motion model to describe the magnitude of the star for the day, t, for a star Delta Cephei.
The magnitude of a star named Delta Cuphea varies from an apparent magnitude of
3.6
to an apparent magnitude of
4.3
with a period of
5.4
days. At
t
=
0
days, the star is at its brightest with a magnitude of
3.6
(on the magnitude scale, brighter objects have a smaller magnitude than dimmer objects). Write a simple harmonic motion model to describe the magnitude
M
of the star for day
t
.
One well-known Cepheid variable is Polaris, the North Star. The apparent magnitude of Polaris varies from an average level of
1.97 with an amplitude of 0.1 and a period of 3.97 days. Make a sine model of the apparent magnitude of Polaris as a function
of time.
(Express numbers in exact form. Use symbolic notation and fractions where needed. Give the equations in terms of t and m,
where t is time measured in days and m is apparent magnitude. Note that t = 0 occurs on a day when the magnitude is
beginning to increase from the average level.)
equation: I
The graph of y = Asec(Bx + C) +D is pictured right; find A, B, C, and D.
Give the amplitude, period, phase shift, and mean value of the associated
cosine function, and graph it on the same axes.
In whoville, the amount of rainfall varies greatly each week and follows a sinusoidal pattern. The following data is the recorded millimeters (mm) of precipitation across 14 weeks. Determine a sine and a cosine function that approximates the amount of rainfall over time in weeks. Decimals are allowed.
Week 1, rainfall(mm) - 1.4
Week 2, rainfall(mm) - 3.1
Week 3, rainfall(mm) - 4.3
Week 4, rainfall(mm) - 2.9
Week 5, rainfall(mm) - 1.2
Week 6, rainfall(mm) - 0.1
Week 7, rainfall(mm) - 1.3
Week 8, rainfall(mm) - 2.7
Week 9, rainfall(mm) - 4.3
Week 10, rainfall(mm) - 3.2
Week 11, rainfall(mm) - 1.1
Week 12, rainfall(mm) - 0.2
Week 13, rainfall(mm) - 1.2
Week 14, rainfall(mm) - 2.8
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