Estimate Spring and Damping Constants of 1700kg Automobile

[mb85]

The suspension system of a 1700 kg automobile "sags" 13 cm when the chassis is placed on it. Also, the oscillation amplitude decreases by 62% each cycle. Estimate the values of (a) the spring constant k and (b) the damping constant b for the spring and shock absorber system of one wheel, assuming each wheel supports 425 kg.

Kx = mg
K = 1281.5 N/m

But the damping constant i am having trouble with.
W' = Square root (K/m - b^2/4m^2) is the formula i think i use?
= kg/s

but both answers are wrong

 

[Hootenanny]

Perhaps if you showed your calculations we could help.

~H

 

[kyle8921]

To estimate the damping constant, we can use the given information about the oscillation amplitude decreasing by 62% each cycle. This means that each cycle, the amplitude is reduced to 38% of its previous value. We can use this to calculate the damping ratio, ζ, using the formula:

ζ = ln(0.38)/ln(0.62) = 0.669

Next, we can use the formula for the natural frequency of a damped harmonic oscillator to calculate the damping constant:

ω_n = √(k/m - ζ^2/4)

Since we already know the values for k and m (from the given information and the formula for the spring constant), we can plug those in to solve for ω_n:

ω_n = √(1281.5/425 - (0.669^2)/4) = 6.72 rad/s

Finally, we can use the formula for the damping constant, b, to solve for the unknown value:

b = 2ζmω_n = 2(0.669)(425)(6.72) = 572.5 kg/s

Therefore, the estimated values for the spring constant and damping constant of the suspension system of the 1700 kg automobile are 1281.5 N/m and 572.5 kg/s, respectively. It is important to note that these are only estimates and the actual values may vary depending on the specific design and components of the suspension system.