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Section 8.5

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1. g \approx 978.9 centimeters per second per second

3. For c = 0 ,

\displaystyle{x = 10\cos(t)}

and the motion is undamped. For c = 10 ,

\displaystyle{x = \frac{20}{\sqrt{3}}e^{\frac{-t}{2}}\cos\left(\frac{\sqrt{3}}{2}t - \frac{\pi}{2}\right)}

and the motion is underdamped. For c = 25 ,

\displaystyle{x = -\frac{10}{3}e^{-2t} + \frac{40}{3}e^{-\frac{t}{2}}}

and the motion is overdamped.

6. (a) Hint: Show that x must satisfy the equation \displaystyle{\ddot{x} + \frac{k}{m}x = 0}, where \displaystyle{k = \frac{mg}{R}}.

(b) 84.5 minutes

(c) -17,614 miles per hour

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