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GrizzlyChicken

  • 2 years ago

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?

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  1. goformit100
    • 2 years ago
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    post the question in physics section Not here @GrizzlyChicken

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

  3. nphuongsun93
    • 2 years ago
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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''

  4. nphuongsun93
    • 2 years ago
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    it's both physics and math lol

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

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

  7. GrizzlyChicken
    • 2 years ago
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    sorry

  8. nphuongsun93
    • 2 years ago
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    still~ same way of solving :P

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

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

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

  12. nphuongsun93
    • 2 years ago
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    yup, that's the initial position

  13. GrizzlyChicken
    • 2 years ago
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    is cos(0)=1?

  14. nphuongsun93
    • 2 years ago
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    yes

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

  16. GrizzlyChicken
    • 2 years ago
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    maybe

  17. nphuongsun93
    • 2 years ago
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    no no, find the derivative of the function x

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

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

  20. GrizzlyChicken
    • 2 years ago
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    and sin(0)=0

  21. GrizzlyChicken
    • 2 years ago
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    so the velocity is 0

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

  23. nphuongsun93
    • 2 years ago
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    do you know how to derivative?

  24. GrizzlyChicken
    • 2 years ago
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    yea, did you use the chain rule?

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

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

  27. nphuongsun93
    • 2 years ago
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    |dw:1349943924669:dw|

  28. nphuongsun93
    • 2 years ago
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    derivative again for the acceleration equation

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

  30. GrizzlyChicken
    • 2 years ago
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    wait

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

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

  33. GrizzlyChicken
    • 2 years ago
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    ohhh

  34. nphuongsun93
    • 2 years ago
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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

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

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

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