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, its speed is 0 feet per second. 1.5 seconds later, the weight is at its furthest from the ground, and its speed is again 0 feet per second. But when the weight is halfway between those points, it reaches its maximum speed of 6 feet per second. The speed of the weight 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=𝑎cos𝑏𝑡+𝑐+𝑑.
Find values of constants 𝑎, 𝑏, 𝑐, and 𝑑.