Question

The equation that models the height above or belowequilibrium in inches, h, of a spring over time in seconds, t, is h = -30cos (2pi/5t). At which times will the spring be at a height of 20 in. above equilibrium? Select all that apply.A. 1.3 secondsB. 1.8 secondsC. 3.2 secondsD. 4.3 secondsE. 5.7 seconds

Answer 1

We need to solve the following expression:

`h=-30\cdot\cos ((2\pi)/(5)\cdot t)`

For when h is equal to 20.

`\begin{gathered} 20=-30\cdot\cos ((2\pi)/(5)t) \\ \cos ((2\pi)/(5)t)=-(2)/(3) \\ \arccos (\cos ((2\pi)/(5)t))=\arccos (-(2)/(3)) \\ (2\pi)/(5)t-2\pi\cdot n=\pm2.3 \\ (2\pi)/(5)t=\pm2.3+2\pi\cdot n \\ t=\pm(11.5)/(2\pi)+5n \\ \text{ For n =0.} \\ t=1.83 \\ \text{For n =1} \\ t=6.83\text{ and }t=3.17 \end{gathered}`

The answers are 1.8 seconds and 3.2 seconds.