Answer
c= 10 gives Underdamping
c = 15 gives Underdamping
c = 20 gives Criticaldamping
c = 25 gives Overdamping
c = 30 gives Overdamping
Work Step by Step
$y'' + cy' + 100y = 0$
To find the type of damping, you have to look for the value of the D.
$D>0 => Overdamping $
$D=0 => Critical damping$
$D>0 => Underdamping$
$D_{c} = \sqrt (c^{2} - 4 \times 1 \times 100) = \sqrt (c^{2}-400) $
So you get the following values by filling in this equation.
$D_{10} = \sqrt (-300)$
$D_{15} = \sqrt (-175)$
$D_{20} = \sqrt 0$
$D_{25} = \sqrt 225 = 15$
$D_{30} = \sqrt (500)$
