[UPSC CSE 2003] Waves (Q58, 30M)

An ideal massless spring of force constant k has a mass m attached to one of its ends, the other and being fixed to a rigid support. The spring is horizontal floor, A resistive force -bv, proportional to the velocity v acts on the mass. Assuming the damping to be light, obtain the frequency of oscillation. When m = 0.1\text{ kg} and k = 10\text{ N/m}, it is found that the frequency of oscillation is \sqrt{1/2} times the frequency in the absence of damping. Calculate the value of the constant b.