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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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?

Mathematics
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Thats D^2x+bDx+9x=0
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
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

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Other answers:

rather, b = + or - 6
As the equation is quadratic, i.e.it is of degree 2, the equation has 2 roots which are '+6' & '-6'
good work aditya!
Thank you! :)

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