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Maximum Acceleration

  1. Nov 13, 2012 #1
    Helping a friend out with some physics 1 mid-semester and It's been a little since I have had a physics course.... so the question is

    "If a 30 g bird lands on a slender branch where it oscillates up and down with simple harmonic motion of amplitude 3.00 x 10^-2m and period 1.2 s"...

    trying to find an equation to solve for max acceleration, expressed as a fraction of the acceleration of Gravity as well as maximum speed... any help would really be appreciated and thanks a lot to anyone that reads this
     
  2. jcsd
  3. Nov 13, 2012 #2

    rock.freak667

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    SHM is defined as

    a= -ω2x


    Thus a will be max when x (displacement) is maximum. So at what value of x will the displacement be maximum?
     
  4. Nov 13, 2012 #3
    I don't have a key and I feel like I may be way off but here is what I have so far

    f= 1/t so F=.83 Hz

    A= (2(3.14)f)^2 x
    so A=27x

    then for X,

    X=Acos2(3.14)f(t)
     
  5. Nov 13, 2012 #4
    wouldn't it be 3?
     
  6. Nov 13, 2012 #5
    or would it be 6? I am confused in what to do with amplitude, if amplitude is 3 cm, that would mean peak to trough is 6 cm? Correct? Is that what I would go with?
     
  7. Nov 13, 2012 #6
    Its asking for the max speed and acceleration of the bird, the thing that throws me off is I don't know if it is asking for the speed the bird landed on the branch or the speed which it actually oscillates
     
  8. Nov 13, 2012 #7

    rock.freak667

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    Right and the maximum value of X is A.
     
  9. Nov 13, 2012 #8
    Ok great, A as in amplitude or acceleration... sorry, thanks again
     
  10. Nov 13, 2012 #9

    rock.freak667

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    A as in amplitude.
     
  11. Nov 14, 2012 #10
    So then, would speed maximum or minimum when the finch hits max acceleration?
     
  12. Nov 14, 2012 #11

    rock.freak667

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    Well when your displacement is zero, you would have maximum velocity.

    Remember the bird is landing from some height. So as it hits, it will be at maximum velocity.

    If we go back to your equation for displacement x=Asin(ωt), how would you find velocity from this?
     
  13. Nov 14, 2012 #12
    makes sense, since the bird has yet to transfer its energy to the branch... Plug in amplitude -sin and multiply with the angular force times time period...?

    So to get this straight, and I really appreciate all of this,

    A as in amplitude
    A= (2(3.14)f)^2 x
    so A=27x

    I would plug A= 27x and then solve for X which would be my maximum acceleration? In this case 3=27x so x would be 9 cm/s

    Maximum Velocity would be the moment before impact?

    The last thing it asks
     
  14. Nov 14, 2012 #13
    is to express it as a fraction of the acceleration of gravity, so just 9cm/s^2?
     
  15. Nov 14, 2012 #14

    rock.freak667

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    No, if x=Asin(ωt), how would you get velocity? Hint: What is the definition of velocity?




    You can express the acceleration as a fraction of gravity as both are acceleration terms. If you want to express velocity in terms of gravity then your units will not make too much sense.
     
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