Critically damped current in this network

[EEZeroo]

Homework Statement

I'm supposed to find whether the current in the following network is

a) under-damped
b) critically damped
c) undamped
c) over-damped

Homework Equations

According to Kirchoff's laws

The Attempt at a Solution

The answer given by my professor for this question is supposed to be "b) critically damped" so I just converted the given values into SI values
R = 1kilo-ohm = 1000 ohm
L = 10mH = 0,01H
C = 40nF = 4 * 10^(-8)

and then I tried relating them to

But I do not find two real roots that are equal for it to be critically damped.

What did I do wrong?

 

[antny]

Critical damping will occur when \alpha^{2}-4\omega^{2}_{o}=0. Another way to write it is: R=sqrt(4*L/C). If you plug in your values for R, L and C, you'll find that it is indeed critically damped.

 

[EEZeroo]

Thank you. I see that my silly mistake was that I substracted the 10 instead of leaving it homogenous.

Though, when exactly is a circuit undamped? I know when it's critically, overdamped or underdamped but when would it be undamped?

 

[antny]

If there's a resistor, there will always be energy lost, hence the damping.
An LC circuit (no resistor) will oscillate without damping.