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:

at t = 5.4485 units (maybe seconds, but it is not given)

Step-by-step explanation:

In the equation, h is the height above/below the rest position and t is the time.

Since we want to know WHEN (t) will it be 3 INCHES ABOVE (h = +3), we can simply plug in 3 into h and solve for t. Shown below:

$h=8Sin(\frac{2\pi}{3t})\\3=8Sin(\frac{2\pi}{3t})\\\frac{3}{8}=Sin(\frac{2\pi}{3t})\\\frac{2\pi}{3t}=Sin^{-1}(\frac{3}{8})\\\frac{2\pi}{3t}=0.3844\\2\pi=1.1532t\\t=\frac{2\pi}{1.1532}\\t=5.4485$

Hence,

At t = 5.4485 seconds (no unit of time is given, i am assuming seconds), the height of the weight will be 3 inches above the rest position.

Answer 2

Answer:

0.18 seconds

Step-by-step explanation: