Question

the height, h, in feet of a ball suspended from a spring as a function of time, t, in seconds can be modeled by the equation h = a*sin(b(t - h))+k. what is the height of the ball at its equilibrium?
○ a feet
○ b feet
○ h feet
○ k feet

Explanation:

Step1: Recall properties of sinusoidal - type functions

The general form of a sinusoidal function for vertical displacement is $h = a\sin(b(t - h))+k$. The sine function $\sin(b(t - h))$ has a range of $[- 1,1]$. At equilibrium, the sinusoidal part $\sin(b(t - h))$ has a value of $0$ because the equilibrium position is the mid - point of the oscillation.

Step2: Calculate the height at equilibrium

When $\sin(b(t - h)) = 0$, we substitute this into the equation $h = a\sin(b(t - h))+k$. Then $h=a\times0 + k=k$.

Answer:

D. $k$ feet