Question

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?

Answer 1

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

Answer 2

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

Answer 3

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

Answer 4

rather, b = + or - 6

Answer 5

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

Answer 6

good work aditya!

Answer 7

Thank you! :)