Finding spring constant, damping constant and Q for suspension of a car

FortisInArdui

1. The problem statement, all variables and given/known data

The suspension of a car (mass= 2000kg) sags a distance of 10cm when the weight of the entire car is placed on it. Also, the amplitude of its oscillations decrease by a factor of 50% over 3 complete oscillations.
a) Find the spring constant(k)
b) Find the damping constant(b)
c) Find the Q for the shock absorber system of one wheel assuming eah wheel supports a quarter of the weight of the car.

I can do parts a and b but I don't know how to do part c


2. Relevant equations

F=kx

damping ratio=b/(2*sqrt(m*k)

A=A₀/(sqrt((1-r²)²+r²/Q²)

Q = w₀*m/b

w₀=sqrt(k/m)
w=w₀*sqrt(1-(b/(2M))²) where w is the frequeny of oscillation




3. The attempt at a solution

a) F=kx
(2000kg)*(9.81m/s²)/(0.10m) =k
k=1.96*10⁵

b)
damping ratio = b/(2*sqrt(m*k))
0.5 = b/(2*sqrt(2000kg*1.96⁵)
b= 1.98*10⁴

c)
I thought that since 1. w₀=sqrt(k/m ) and 2. Q= w₀*/b that the first equation can be substituted into the second equation to get 3. Q=sqrt(k/m)*m/b.
I didn't get the right answer using equation 3 so I'm wondering if I used the wrong formulas.

Any suggestions would be greatly appreciated.