Question

8-23. Cooper Toy Company has designed a new toy that oscillates up and down and its position can be modeled by a sinusoidal curve. At time t = 5 seconds, the toy is at its maximum height, 18 cm above the ground. Four seconds later, the toy is at its minimum height, 6 cm above the ground. Write an equation to model the height, in centimeters of the toy at any time t, in seconds.

Answer 1

Given data:

The maximum height of the toy at t=5 seconds is M= 18 cm.

The minimum height of the toy at t=9 seconds is m=6 cm.

The expression for the amplitude is,

`\begin{gathered} A=(M-m)/(2) \\ =(18-6)/(2) \\ =6 \end{gathered}`

The expression for the mean value is,

`\begin{gathered} x=(18+6)/(2) \\ =12 \end{gathered}`

The period of the given curve is,

`\begin{gathered} P=(2\pi)/(10) \\ =(\pi)/(5) \end{gathered}`

The equation for the given curve is,

`y=6\cos ((\pi)/(5)(t-4))+12`

Thus, equation of the given curve is y=6 cos(π(t-4)/5)+12.