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anonymous
 one year ago
5 owlbucks
An object attached to a coiled spring is pulled down a distance 10 units from its rest position and then released. Assuming that the motion is simple harmonic with a period T= 8 seconds, write an equation that relates the displacement d of the object from its rest position after t seconds. Also assume that the direstion of positive motion is up.
anonymous
 one year ago
5 owlbucks An object attached to a coiled spring is pulled down a distance 10 units from its rest position and then released. Assuming that the motion is simple harmonic with a period T= 8 seconds, write an equation that relates the displacement d of the object from its rest position after t seconds. Also assume that the direstion of positive motion is up.

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BTaylor
 one year ago
Best ResponseYou've already chosen the best response.1Because it is simple harmonic motion, we know we will have a sinusoidal (ie., sine or cosine) function. It will take the form \(y(t) = a \sin(bt + c) \).

BTaylor
 one year ago
Best ResponseYou've already chosen the best response.1In this equation \(y(t) = a \sin(bt + c)\): \(a\) is the amplitude of the motion. Since you are pulling it down a distance of 10 units, the object will oscillate between 10 and +10 units, so the amplitude is 10. \(b\) modifies the period of the motion. It follows the formula \(\text{period} = 2 \pi \times b\). Since we know the period is 8, you can find \(b\) by dividing 8 by \(2 \pi\). \(c\) modifies the phase shift. Once you've found \(a\) and \(b\), you can plug in your initial value (position = 10 @ t = 0) to find \(c\).

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0This is what I got and I believe it is correct. \( \large d = 10 cos(\frac{\pi}{4}t) \)

BTaylor
 one year ago
Best ResponseYou've already chosen the best response.1That is correct. Also, good choice using cosine instead of sine. Removes the whole phase shift issue.

BTaylor
 one year ago
Best ResponseYou've already chosen the best response.1In the future, I would graph it (desmos.com/calculator) to make sure it matches all your requirements.
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