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GrizzlyChicken

The position of a mass on a spring (relative to equilibrium) at time t <= 0 is x(t) = 2 cos((pi)t) where x is in centimeters and t is in seconds. Answer the ques- tions. Include units! (a) What is the initial position of the mass? (b) What is the initial velocity of the mass? (c) What is the initial acceleration of the mass? (d) Does the mass initially move towards the wall or away from it? (e) At what point does the mass rst turn around?

  • one year ago
  • one year ago

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  1. goformit100
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    post the question in physics section Not here @GrizzlyChicken

    • one year ago
  2. GrizzlyChicken
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    its in my calc book, isn't this math?

    • one year ago
  3. nphuongsun93
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    a) put t = 0 and solve for x b) find x' and put t = 0 and solve for x' c) find x'' and put y = 0 and solve for x''

    • one year ago
  4. nphuongsun93
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    it's both physics and math lol

    • one year ago
  5. nphuongsun93
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    *typo fix* sorry c) find x'' and put t=0

    • one year ago
  6. GrizzlyChicken
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    wait, its x(t)=2cos((pi)(t))

    • one year ago
  7. GrizzlyChicken
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    sorry

    • one year ago
  8. nphuongsun93
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    still~ same way of solving :P

    • one year ago
  9. GrizzlyChicken
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    damn, theres another error, i'm gonna look it all over again, for some reason copy and pasting changed everything

    • one year ago
  10. GrizzlyChicken
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    at time t is greater or equal to 0. its right now

    • one year ago
  11. GrizzlyChicken
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    so if i put 0 for t, its 2cos(0)

    • one year ago
  12. nphuongsun93
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    yup, that's the initial position

    • one year ago
  13. GrizzlyChicken
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    is cos(0)=1?

    • one year ago
  14. nphuongsun93
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    yes

    • one year ago
  15. GrizzlyChicken
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    then for b) derivative of 2 is 0 so its all 0

    • one year ago
  16. GrizzlyChicken
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    maybe

    • one year ago
  17. nphuongsun93
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    no no, find the derivative of the function x

    • one year ago
  18. GrizzlyChicken
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    so the derivative of 2cos(pi*0)?

    • one year ago
  19. GrizzlyChicken
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    which uses the product rule (0)(cos...)+(2)(-sin(0))

    • one year ago
  20. GrizzlyChicken
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    and sin(0)=0

    • one year ago
  21. GrizzlyChicken
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    so the velocity is 0

    • one year ago
  22. nphuongsun93
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    wops sorry i'm here x = 2 cos (pi t) x' = -2 pi sin (pi t)

    • one year ago
  23. nphuongsun93
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    do you know how to derivative?

    • one year ago
  24. GrizzlyChicken
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    yea, did you use the chain rule?

    • one year ago
  25. GrizzlyChicken
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    is that why pi is with -2?

    • one year ago
  26. nphuongsun93
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    no chain rule. derivative of cos is -sin. pi 's brought out when derivative.

    • one year ago
  27. nphuongsun93
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    |dw:1349943924669:dw|

    • one year ago
  28. nphuongsun93
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    derivative again for the acceleration equation

    • one year ago
  29. GrizzlyChicken
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    -2cos(pi*t)

    • one year ago
  30. GrizzlyChicken
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    wait

    • one year ago
  31. GrizzlyChicken
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    -2pi*cos(pi*t)

    • one year ago
  32. nphuongsun93
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    almost correct, but now pi is brought one more time so it's -2 pi^2 cos (pi t)

    • one year ago
  33. GrizzlyChicken
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    ohhh

    • one year ago
  34. nphuongsun93
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    x = 2 cos (pi t) x0 = 2 x' = v = -2 pi sin (pi t) v0 = 0 x'' = a = -2 pi^2 cos (pi t) a0 = -2pi^2 and idk how to do d and e

    • one year ago
  35. GrizzlyChicken
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    does the mass move toward the wall because the acceleration is negative?

    • one year ago
  36. GrizzlyChicken
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    oh, thats alright. you've helped me enough.Thanks!

    • one year ago
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