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Oscillation Question

  1. Nov 23, 2006 #1
    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
     
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  3. Nov 23, 2006 #2

    Hootenanny

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    HINT: Hooke's Law
     
  4. Nov 25, 2006 #3
    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.
     
  5. Nov 27, 2006 #4
    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
     
  6. Nov 27, 2006 #5

    Hootenanny

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    I think that the following equation may be more useful.

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

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

    Now, from the above equation we can see that at t = 0 [itex]x=x_m[/itex], yes? If we then assume that [itex]b<<\sqrt{km}[/itex], 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 xm has decrease by 43%. Can you go from here?
     
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