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Question 14.2: Car springs again. Determine the period and frequency of the......

Car springs again. Determine the period and frequency of the car in Example 14-1a after hitting a bump. Assume the shock absorbers are poor, so the car really oscillates up and down.

APPROACH We put m=1400 \mathrm{~kg} and k=6.5 \times 10^{4} \mathrm{~N} / \mathrm{m} from Example 14-1a into Eqs. 14-7.

\begin{aligned}f & =\frac{1}{2 \pi} \sqrt{\frac{k}{m}} & (14-7a)\\T & =2 \pi \sqrt{\frac{m}{k}} & (14-7b)\end{aligned}

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From Eq. 14-7 b,

T=2 \pi \sqrt{\frac{m}{k}}=2 \pi \sqrt{\frac{1400 \mathrm{~kg}}{6.5 \times 10^{4} \mathrm{~N} / \mathrm{m}}}=0.92 \mathrm{~s}

or slightly less than a second. The frequency f=1 / T=1.09 \mathrm{~Hz}.

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