Question

A weight is attached to a spring that is fixed to the floor. The equationh= 7 cos (pi/3 t) models the height, h, in centimeters after t seconds of the weight being stretched and released.a. Solve the equation for t.b. Find the times at which the weight is first at a height of 1 cm, of 3 cm, and of 5 cm above the rest position. Round your answers to the nearest hundredth.

Answer 1

The given equation is:

`h=7\cos((\pi)/(3)t)`

Divide both sides of the equation by 7:

`\begin{gathered} \cos((\pi)/(3)t)=(h)/(7) \\ (\pi)/(3)t=\cos^(-1)((h)/(7)) \\ t=(3)/(\pi)\cos^(-1)((h)/(7)) \\ \end{gathered}`
`t=(3)/(\pi)\cos^(-1)((h)/(7))`

When h = 1

`t=78.10s`

When h = 3:

`t=61.71s`

When h=5

`t=42.41s`

h=1, t =78.10;

h=3, t=61.71;

h=5, t=42.41

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