Optimizing Automobile Suspension: Calculating Spring and Damping Constants

[cd80187]

The suspension system of a 1700 kg automobile "sags" 13 cm when the chassis is placed on it. Also, the oscillation amplitude decreases by 43% 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.

I have looked at this problem for awhile, and I have no clue where to even start... So I was just looking for a little help to get started in the right place, thank you in advance

 

[Hootenanny]

HINT: Hooke's Law

 

[MT1986]

Alright, I have the same question. After applying Hooke's Law I think i found the spring constant, which is fairly straightforward. Now, how do i find the damping constant? I'm a little unclear as to which equation to use, because they have more then one unknown variable.

 

[cd80187]

I was able to solve the first part, but I could not get the second part. The book gives us two equations, and I think I am supposed to use this one : omega (w) = Square root of (k/m - b squared/4msquared). But beyond that, I am unsure what I am supposed to do

 

[Hootenanny]

I think that the following equation may be more useful.

x(t)=x_m\cdot e^{-bt/2m}\cos(\omega\cdot t)

where x is the displacement, x_m is the amplitude, and I'm sure you know the rest...

Now, from the above equation we can see that at t = 0 x=x_m, yes? If we then assume that b<<\sqrt{km}, then the period of the springs is approximately that of an undamped mass-spring system, therefore we can calculate the time period of the oscillator. And you know that after one time period that x_m has decrease by 43%. Can you go from here?