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

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.
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 Tags car, damping ratio, oscillations, spring constant