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theEric

  • 2 years ago

Hi! I have to find the velocity as a function of displacement for some given force functions. Here is the question: Find the velocity \(\dot x\) as a function of the displacement \(x\) for a particle of mass \(m\), which starts from rest at \(x=0\), subject to the following force functions:

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  1. theEric
    • 2 years ago
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    One moment!

  2. theEric
    • 2 years ago
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    (a) \(F_x=F_0+cx\) (c) \(F_x=F_0\cos(cx)\) If I see the general technique, I might be able to get it! Thanks!

  3. Saeeddiscover
    • 2 years ago
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    You can use this relation

  4. Saeeddiscover
    • 2 years ago
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    |dw:1379923967464:dw|

  5. theEric
    • 2 years ago
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    Ah, thank you very much Saeeddiscover!

  6. Saeeddiscover
    • 2 years ago
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    Hold on a moment!

  7. theEric
    • 2 years ago
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    Okay!

  8. theEric
    • 2 years ago
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    Does that work out? Is the \(x\) in \(F_x=F_0+c\large x\) a function of \(t\)?

  9. Saeeddiscover
    • 2 years ago
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    For the second one, you may consider this way as well: |dw:1379924739346:dw|

  10. theEric
    • 2 years ago
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    Thank you!

  11. Saeeddiscover
    • 2 years ago
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    Please wait a moment. I got a mistake!

  12. theEric
    • 2 years ago
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    Okay! If it's in that last part, I can't find it because I don't know that material yet!

  13. Saeeddiscover
    • 2 years ago
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    |dw:1379925139264:dw|

  14. Saeeddiscover
    • 2 years ago
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    |dw:1379925286166:dw|

  15. theEric
    • 2 years ago
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    That all makes sense, thank you! I'll try to apply those to my problems soon!

  16. theEric
    • 2 years ago
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    I think I need to head to bed, though...

  17. theEric
    • 2 years ago
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    Thanks again! :)

  18. Saeeddiscover
    • 2 years ago
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    Both 1 and 2 you are given simply can be solved using the last equation I gave you. It is true and works properly.

  19. theEric
    • 2 years ago
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    Great! I will use that, then! Have a good day!

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