Answered

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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

The Equation That Models The Height Above Or Belowequilibrium In Inches H Of A Spring Over Time In Seconds T Is H 30cos 2pi5t At Which Times Will The Spring Be class=

Sagot :

We need to solve the following expression:

[tex]h=-30\cdot\cos (\frac{2\pi}{5}\cdot t)[/tex]

For when h is equal to 20.

[tex]\begin{gathered} 20=-30\cdot\cos (\frac{2\pi}{5}t) \\ \cos (\frac{2\pi}{5}t)=-\frac{2}{3} \\ \arccos (\cos (\frac{2\pi}{5}t))=\arccos (-\frac{2}{3}) \\ \frac{2\pi}{5}t-2\pi\cdot n=\pm2.3 \\ \frac{2\pi}{5}t=\pm2.3+2\pi\cdot n \\ t=\pm\frac{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}[/tex]

The answers are 1.8 seconds and 3.2 seconds.

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