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Q. 6

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Precalculus Enhanced with Graphing Utilities

Found in: Page 549

Book edition 6th

Author(s) Sullivan

Pages 1200 pages

ISBN 9780321795465

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Short Answer

an object attached to a coiled spring is pulled down a distance a from its rest position and then released. Assuming that the motion is simple harmonic with period T, write an equation that relates the displacement d of the object from its rest position after t seconds. Also assume that the positive direction of the motion is up:
$a = 10, T = 3 s e c o n d s$

The equation of distance is $d = - 10 \cos (\frac{2 π}{3})$

See the step by step solution

Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Step 1: Given information

We are given $a = 10, T = 3 s e c o n d s$

Step 2: Find the equation

The object starts at a position 10 units distance below the resting position so $a = - 10$

Also it starts with amplitude position we will use the cosine function

Now we find $ω$

$ω = \frac{2 π}{T} ω = \frac{2 π}{3}$

Hence the equation can be given as role="math" localid="1646654788496" $d = - 10 \cos (\frac{2 π}{3} t)$

Step 3: Conclusion

The equation can be given as $d = - 10 \cos (\frac{2 π}{3} t)$

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