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Q. 7

Expert-verified

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:
$a = 6, T = π s e c o n d s$

The equation can be given as $d = - 6 \cos (2 t)$

See the step by step solution

Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Step 1: Given information

We are given $a = 6, T = π s e c o n d s$

Step 2: Find the equation

An object suspended from spring pulled down Hence $a = - 6$

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

Now we find $ω$

$ω = \frac{2 π}{T} ω = \frac{2 π}{π} w = 2$

The equation can be given as $d = - 6 \cos (2 t)$

Step 3: Conclusion

The equation of motion can be given as $d = - 6 \cos (2 t)$

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