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Q. 6

Expert-verifiedFound in: Page 549

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 $d=-10\mathrm{cos}\left(\frac{2\pi}{3}\right)$

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

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" $d=-10\mathrm{cos}\left(\frac{2\pi}{3}t\right)$

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

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