Respuesta :
The equation of the sinusoidal function is 7 × sin((π/15)·(x - 2.5)) + 9
Question: The likely missing parameters in the question are;
The time at which the shorts are at the maximum height, t₁ = 10 seconds
The time at which the shorts are at the minimum height, t₂ = 25 seconds
- The general form of a sinusoidal function is A·sin(B(x - h)) + k
Where;
A = The amplitude
The period, T = 2·π/B
The horizontal shift = h
The vertical shift = k
The parent equation of the sine function = sin(x)
We find the values of the variables, A, B, h, and k as follows;
The given parameters of the sinusoidal function are;
The maximum height = 16 meters at time t₁ = 10 seconds
The minimum height = 2 meters at time t₂ = 25 seconds
The time it takes the shorts to complete a cycle, (maximum height to maximum height), the period, T = 2 × (t₂ - t₁)
∴ T = 2 × (25 - 10) = 30
The amplitude, A = (Maximum height- Minimum height)/2
∴ A = (16 m - 2 m)/2 = 7 m
The amplitude of the motion, A = 7 meters
T = 2·π/B
∴ B = 2·π/T
T = 30 seconds
∴ B = 2·π/30 = π/15
B = π/15
At t = 10, y = Maximum
Therefore;
sin(B(x - h)) = Maximum, which gives; (B(x - h)) = π/2
Plugging in B = π/15, and t = 10, gives;
((π/15)·(10 - h)) = π/2
10 - h = (π/2) × (15/π) = 7.5
h = 10 - 7.5 = 2.5
h = 2.5
The minimum value of a sinusoidal function, having a centerline of which is on the x-axis, and which has an amplitude, A, is -A
Therefore, the minimum value of the motion of the turbine blades before, the vertical shift = -A = -7
The given minimum value = 2
The vertical shift, k = 2 - (-7) = 9
Therefore, k = 9
Therefore;
The equation of the sinusoidal function is 7 × sin((π/15)·(x - 2.5)) + 9
More can be learned about sinusoidal functions on Brainly here;
https://brainly.com/question/14850029
