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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.

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  1. BTaylor
    • one year ago
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    Because it is simple harmonic motion, we know we will have a sinusoidal (ie., sine or cosine) function. It will take the form \(y(t) = a \sin(bt + c) \).

  2. BTaylor
    • one year ago
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    In 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 \(c\).

  3. anonymous
    • one year ago
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    This is what I got and I believe it is correct. \( \large d = -10 cos(\frac{\pi}{4}t) \)

  4. anonymous
    • one year ago
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    Do you concur?

  5. BTaylor
    • one year ago
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    That is correct. Also, good choice using cosine instead of sine. Removes the whole phase shift issue.

  6. BTaylor
    • one year ago
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    In the future, I would graph it (desmos.com/calculator) to make sure it matches all your requirements.

  7. anonymous
    • one year ago
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    Cool, thank you.

  8. anonymous
    • one year ago
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    5 Owlbucks sent!

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