Question

The motion of a weight that hangs from a spring is represented by the equation h=8sin(2pi/3t). It models the weight’s height above or below the rest position as a function of time. Approximately when will the object be 3 inches above the rest position?

Answer 1

Answer:

0.18 seconds

Step-by-step explanation:

Answer 2

Using the given function, it is found that the object will be 3 inches above the rest position after 0.18 seconds.

What is the function?

The function for an object's height after t seconds is given by:

$h(t) = 8\sin{\left(\frac{2\pi}{3}t\right)}$

The height is of 3 inches when h(t) = 3, hence:

$h(t) = 8\sin{\left(\frac{2\pi}{3}t\right)}$

$3 = 8\sin{\left(\frac{2\pi}{3}t\right)}$

$\sin{\left(\frac{2\pi}{3}t\right)} = \frac{3}{8}$

$\sin^{-1}{\sin{\left(\frac{2\pi}{3}t\right)}} = \sin^{-1}{\left(\frac{3}{8}\right)}$

$\frac{2\pi}{3}t = 0.3844$

$t = \frac{3 \times 0.3844}{2\pi}$

$t = 0.18$

The object will be 3 inches above the rest position after 0.18 seconds.

More can be learned about functions at https://brainly.com/question/25537936