What value of c will cause the system to be critically damped?

In the figure above, let k = 4000 N/m, 1₁ =1.5m and l₂ = .5m, 1 = 1m, and m = 40kg. This time,

consider the beam to have a mass of 40 kg (The length of the beam is 1+4) It is pivoted about O and is

assumed to be rigid.