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

In summary, the suspension of a 2000kg car sags 10cm when the car's weight is placed on it, and its oscillations decrease by 50% over 3 complete oscillations. The spring constant is 1.96*10^5 and the damping constant is 1.98*10^4. The Q for the shock absorber system of one wheel is not known, but can be found using the equations Q = sqrt(k/m)*m/b.
  • #1
FortisInArdui
1
0

Homework Statement



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

Homework 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

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.:smile:
 
Last edited:
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  • #2
FortisInArdui said:
0.5 = b/(2*sqrt(2000kg*1.965)
the 50% was over three oscillations.
 

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

What is the purpose of finding the spring constant, damping constant, and Q for suspension of a car?

The spring constant, damping constant, and Q are important parameters used to characterize the behavior of a car's suspension system. The spring constant determines the stiffness of the suspension, the damping constant controls the amount of energy dissipated during vibrations, and the Q factor represents the quality of the suspension's response.

How are these parameters usually calculated?

The spring constant is typically calculated by measuring the force required to compress or extend the spring and relating it to the change in length. The damping constant can be determined by analyzing the decay of vibrations in the suspension system. The Q factor can be calculated using the spring and damping constants, along with the natural frequency of the suspension.

What factors can affect the accuracy of these calculations?

The accuracy of the calculations can be affected by various factors such as temperature, material properties, and manufacturing tolerances. It is important to make sure that the measurements are taken under controlled conditions and that the correct values for the materials are used in the calculations.

How do these parameters impact the performance of a car's suspension?

The spring constant affects the stiffness of the suspension, which can impact the handling and stability of the car. The damping constant determines how quickly the suspension can absorb and dissipate energy, which can affect the ride comfort. The Q factor reflects the responsiveness and smoothness of the suspension's movements.

Are there any industry standards for these parameters?

Yes, there are industry standards for these parameters that are used in the design and testing of car suspensions. These standards help ensure that the suspension system meets safety and performance requirements. However, the specific values may vary depending on the type of car and its intended use.

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