A 20lb weight hangs from the end of a spring. Jania stretches it downward so that the weight is 8 feet from the top of the system. From there, she releases it (𝑡=0). The weight begins bobbing up and down. When the weight is at its closest to the ground, the weight is 8 feet from the top of the system. When the weight is at its furthest from the ground, the weight is 2 feet from the top of the system. The weight continues bobbing up and down, completing 20 cycles of the pattern every 60 seconds. The distance between the weight and the top of the system 𝑡 seconds after the weight is released can be modelled by a sinusoidal function ℎ𝑡.
The function ℎ can be written in the form ℎ𝑡=𝑎sin𝑏𝑡+𝑐+𝑑.
Find values of constants 𝑎, 𝑏, 𝑐, and 𝑑.