An object of mass 0.2kg is hung from a spring whose spring constant is 80N/m. The object is subject to a resistive force given by -bv, where v is it's velocity in meters per second.
If the damped frequency is √(3)/2 of the undamped frequency, what is the value of b?
The Attempt at a Solution
I tried to write the sum of the forces of the system and got ∑F=-kx-bv=ma
I rewrote it as -kx=b(dx/dt)+m(d^2x/dt^2)
Now I don't have much experience with differential equations but I know the solution is x(t)=Ae^(γt)cos(ωt) where γ=(-b/2m). I also know that the damped frequency is (√(3)/2)√k/m given from the problem. I not sure where to go from here. I am supposed to use the solution and solve for b? Any help would be appreciated.