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Homework Help: Mass/Spring System Damping Constant

  1. Apr 4, 2010 #1
    A mass weighing 32 pounds stretches a spring 6 inches. The spring constant is equal to 64 lb/ft.The mass moves through a medium offering a damping force that is numerically equal to [tex]\beta[/tex] times the instantaneous velocity. Determine the values of [tex]\beta[/tex]>0 for which the spring/mass system will exhibit oscillatory motion.



    2*[tex]\lambda[/tex]=[tex]\frac{\beta}{m}[/tex]

    [tex]\omega[/tex][tex]^{2}[/tex]=[tex]\frac{k}{m}[/tex]

    [tex]\lambda[/tex][tex]^{2}[/tex] - [tex]\omega[/tex][tex]^{2}[/tex]>0 is overdamped

    [tex]\lambda[/tex][tex]^{2}[/tex] - [tex]\omega[/tex][tex]^{2}[/tex]=0 is critically damped

    [tex]\lambda[/tex][tex]^{2}[/tex] - [tex]\omega[/tex][tex]^{2}[/tex]<0 is underdamped

    1 slug = 32 pounds

    I've solved that [tex]\beta[/tex] is equal/less than/greater than 2*[tex]\sqrt{k*m}[/tex]=32, but I don't understand when it will or will not have oscillatory motion.
     
  2. jcsd
  3. Apr 4, 2010 #2

    jack action

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    Underdamped --> There is an oscillatory motion
    Overdamped --> No oscillatory motion (gradually goes to final position)

    So the limit that separates the two is the critically damped situation.
     
  4. Apr 4, 2010 #3
    Thank you!
     
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