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Hard Boiled egg on a spring

  1. Jun 23, 2011 #1
    a 50 g Hard Boiled egg moves on the end of a spring with force constant k=25N/m. Its intial displacement is .3m. A damping force F=-bv acts on the egg and the amplitude of the motion decreases to .1 m in 5 sec. Calculate the magnitue of the damping contant b.

    How exactly do you go about doing this?
    I havent been able to get anywhere on it.
     
  2. jcsd
  3. Jun 24, 2011 #2
    Start with the solution of the equation of motion for this system.
     
  4. Jun 24, 2011 #3
    so we have

    x=Ae^-(b/2m)t cos(w't+phi)

    where w'=(k/m -b^2/4m^2)^1/2

    so heres the problem do you use the initial conditions to solve for b or the final positions, does it make a difference?
     
  5. Jun 24, 2011 #4
    Before you can solve for b you have to apply the initial conditions to solve for A beforehand. Just assume phi is 0.

    Once you have the value for A, solve for b using the other informations given (btw, dont assume that those are for the final position).
     
  6. Jun 25, 2011 #5
    isnt A=.3 since thats the starting position
    i put it into a function solver and i got
    2.94587866888,

    does that seem right?

    also i didnt use the .1 if i was suppose too
     
  7. Jun 25, 2011 #6
    :smile: Lol...I advise you to analytically or numerically solve this problem as I doubt your teacher would accept your answer. I admit solving for b is a bit tedious but you already got A! Keep on working...

    Also usually [itex]0\leq b\leq 1[/itex].

    Hint: Work with the amplitude of oscillation component of your equation instead of working with the whole thing.
     
  8. Jun 25, 2011 #7
    ok so ignoring the cos stuff i got

    .2197224577

    is this one right?

    its in the interval
     
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