Answer:
[tex]D(t) = 9(0.93)^t cos(30 \pi t)[/tex]
Explanation:
Amplitude begins at 9 cm, [tex]A_0 = 9 cm[/tex]
The amplitude decreases by 7% (0.07) each second
The amplitude function can then be modeled as:
[tex]A(t) = A_0(1 - 0.07)^t\\A(t) = 9(0.93)^t[/tex]
The spring oscillates 15 times each second, the period of oscillation (time to make 1 oscillation) will therefore be calculated as:
T = 1/15
[tex]\frac{2\pi }{B} = \frac{1}{15} \\\\B = 30\pi[/tex]
The graphical equation of the system described is:
[tex]D(t) = A cos ( Bt - C) + D[/tex]
Horizontal shift, C = 0
Vertical shift, D = 0
[tex]D(t) = 9(0.93)^t cos(30 \pi t)[/tex]
