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anonymous

  • 5 years ago

What must be the value of b so that the motion of an object given by the equation D2x + bDx + 9x = 0 is critically damped?

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  1. anonymous
    • 5 years ago
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    Thats D^2x+bDx+9x=0

  2. anonymous
    • 5 years ago
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    D^2x+bDx+9x=0 can be written as x"+bx'+9x=0 so we solve for the corresponding quadratic equation: r^2+br+9=0

  3. anonymous
    • 5 years ago
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    the roots are r1 = -b+sqrt(b^2-4ac)/2a and r2 = -b-sqrt(b^2-4ac)/2a for a critically damped system, b^2 = 4ac or b^2 = 4*1*9=36 or b =6

  4. anonymous
    • 5 years ago
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    rather, b = + or - 6

  5. anonymous
    • 5 years ago
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    As the equation is quadratic, i.e.it is of degree 2, the equation has 2 roots which are '+6' & '-6'

  6. anonymous
    • 5 years ago
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    good work aditya!

  7. anonymous
    • 5 years ago
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    Thank you! :)

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