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Max. Net Force

  1. Dec 6, 2009 #1
    The position of a .64 kg mass undergoing simple harmonic motion is given by x(t) = (.16 m)cos([tex]\pi[/tex]t/16). What is the maximum net force on the mass as it oscillates? (hints: First, match the quantities in the equation above to x(t) = Acos([tex]\omega[/tex]t). Next, recall that the max. net force equals the product of the mass and the maximum acceleration.)

    * 3.9 x 10-3 N
    * 9.9 x 10-3 N
    * 1.3 x 10-3 N
    * 6.3 N


    I don't really understand this problem and I need some help. So if anyone would be willing to help, I would really appreciate it. Where do I begin?
     
  2. jcsd
  3. Dec 6, 2009 #2

    rock.freak667

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    well you know F=ma.

    You don't have an expression for a. You know [itex]x(t)=0.16cos(\frac{\pi t}{16})[/itex]. Can you find a(t)?
     
  4. Dec 6, 2009 #3
    I don't understand how. Would it look anything like the x(t) one?
     
  5. Dec 6, 2009 #4

    rock.freak667

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    x is a displacement. Do you know how to get velocity from displacement?
     
  6. Dec 6, 2009 #5
    Not that I know of. Please explain it to me.
     
  7. Dec 6, 2009 #6

    rock.freak667

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    velocity is the rate of change of displacement: v= dx/dt

    acceleration is the rate of change of velocity. Can you find acceleration now?
     
  8. Dec 6, 2009 #7
    So: a = dv/dt?

    But how does that help me with this?
     
  9. Dec 6, 2009 #8
    Maybe try working on one of these problems at a time ;-D.

    Acceleration and force will be maximal when a is at a maximum. Do you know how to do derivatives and do max/min problems?
     
  10. Dec 6, 2009 #9
    No I do not. :frown:
     
  11. Dec 6, 2009 #10

    rock.freak667

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    well find a(t). Now think, cosine and sine are maximum when they equal to what number?
     
  12. Dec 6, 2009 #11
    I still don't understand how to do that when we don't know x, t, or v.
     
  13. Dec 6, 2009 #12

    rock.freak667

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    [tex]x=0.16cos(\frac{\pi t}{16})[/tex]


    do you understand how to differentiate a function?
     
  14. Dec 6, 2009 #13
    No. How do I do that, and how does that help me with this (I mean where do I apply it)?
     
  15. Dec 6, 2009 #14

    rock.freak667

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    The entire problem relies on your knowledge of calculus. I must ask, if you do not know how to find the derivative of a function, how did you get this problem as homework?
     
  16. Dec 6, 2009 #15
    I don't know any calculus. I have only taken Algebra and Trig., and my teacher gave me these, so they must be using things I know, or should know. Any way you can explain that more in terms I can understand?
     
  17. Dec 6, 2009 #16

    rock.freak667

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    read about is http://www.intmath.com/Differentiation/Differentiation-intro.php" [Broken]
     
    Last edited by a moderator: May 4, 2017
  18. Dec 6, 2009 #17
    Okay, I think I understand it a little better now. But where and how do I apply that to this problem?
     
  19. Dec 6, 2009 #18

    rock.freak667

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    read http://www.analyzemath.com/calculus/Differentiation/trigonometric.html" [Broken] as well
     
    Last edited by a moderator: May 4, 2017
  20. Dec 6, 2009 #19
    Okay, but I am still completely lost on this...
     
  21. Dec 6, 2009 #20

    rock.freak667

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    Read up on differentiation some more. But for this problem you need to know these

    y=sinkx, dy/dx=kcoskx

    y=coskx, dy/dx=-ksinkx.

    With these can you find a(t) given x(t)?
     
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