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
.
The maximum angle of the sun above the horizon for a small town in Ontario was recorded on the 21st of each month and is displayed in the table below. Graph the data and create a sinusoidal equation to model the data.
Month
1
2
3
4
5
6
7
8
9
10
11
12
Angle
25
35
45
56
65
68
65
56
45
35
25
22
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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