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Expert-verified Found in: Page 549 ### Precalculus Enhanced with Graphing Utilities

Book edition 6th
Author(s) Sullivan
Pages 1200 pages
ISBN 9780321795465 # 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:$a=10,T=3seconds$

The equation of distance is $d=-10\mathrm{cos}\left(\frac{2\pi }{3}\right)$

See the step by step solution

## Step 1: Given information

We are given $a=10,T=3seconds$

## 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 $\omega$

$\omega =\frac{2\pi }{T}\phantom{\rule{0ex}{0ex}}\omega =\frac{2\pi }{3}\phantom{\rule{0ex}{0ex}}$

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

## Step 3: Conclusion

The equation can be given as $d=-10\mathrm{cos}\left(\frac{2\pi }{3}t\right)$ ### Want to see more solutions like these? 