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Damping coefficient

  1. Oct 9, 2004 #1
    A 50.0-g hard-boiled egg moves on the end of a spring with force constant . It is released with an amplitude 0.300 m. A damping force acts on the egg. After it oscillates for 5.00 s, the amplitude of the motion has decreased to 0.100 m.Calculate the magnitude of the damping coefficient . Express the magnitude of the damping coefficient numerically in kilograms per second, to three significant figures

    pls who can help me?
    thanx
     
  2. jcsd
  3. Oct 9, 2004 #2

    arildno

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    How should Newton's 2.law of motion look like?
     
  4. Oct 9, 2004 #3
    i think it is:
    -kx-bv=ma
     
  5. Oct 9, 2004 #4

    arildno

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    That's correct!
    Now, what type of solutions have you learnt that this differential equation has?
     
  6. Oct 9, 2004 #5

    Pyrrhus

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    See it as

    [tex] -kx - b \frac{dx}{dt} = m\frac{d^2 x}{dt^2} [/tex]
     
    Last edited: Oct 9, 2004
  7. Oct 9, 2004 #6

    Pyrrhus

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    You're right, thanks alridno :smile:
     
  8. Oct 9, 2004 #7
    v= dx/dt and a= d^2/dt^2
     
  9. Oct 9, 2004 #8
    but what is the answer of d^2/dt^2 then?
     
  10. Oct 9, 2004 #9

    arildno

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    mlee:
    Any progress at what sort of solutions your equation has?
     
  11. Oct 9, 2004 #10
    uh not really...;(
     
  12. Oct 9, 2004 #11

    arildno

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    Now, I'd like you try a solution of the form:
    [tex]x(t)=Ae^{rt}[/tex] (A and r constants)
    What condition must be placed on "r" in order for this to be a solution.
    Please post your work.
     
  13. Oct 9, 2004 #12
    Asin(wt)+Bcos (wt)
     
  14. Oct 9, 2004 #13

    arildno

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    This is a solution of an UNDAMPED, harmonic oscillator.
    Your oscillator is NOT undamped; try my approach, and post your work.
     
  15. Oct 9, 2004 #14
    Ae-bt/2mCos(ω't + φ)
     
  16. Oct 9, 2004 #15
    Ae^(bt/2m)*cos(w't+φ)
     
  17. Oct 9, 2004 #16

    arildno

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    You lack a minus sign in your exponential!
    Now, knowing
    a) The initial displacement
    and
    b)That the initial velocity is zero
    How can you determine [tex]A,\phi[/tex]

    Besides, what is your value of "w"?
     
  18. Oct 9, 2004 #17
    ω = sqrt(k/m)
    ω' = √((k/m) - (b²/4m²))
     
  19. Oct 9, 2004 #18

    arildno

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    Now, so how does your initial conditions determine [tex]A,\phi[/tex]?
     
  20. Oct 9, 2004 #19
    i dunno how to find [tex]phi[/tex]
     
  21. Oct 9, 2004 #20
    and w' = 5*10^2-(b^2/1*10^-2)
    is that right?
     
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