The suspension system of a 2000 kg automobile \"sags\" 10 cm when thechassis is

Question

The suspension system of a 2000 kg automobile "sags" 10 cm when thechassis is placed on it. Also, the oscillation amplitude decreasesby 50% each cycle. Estimate the values of (a) the spring constantk and (b) the damping constant b for the springand shock absorber system of one wheel, assuming each wheelsupports 500 kg.

For part (a), my attempts have gone so far as to set mg=-kx.
For part (b), I've gotten x(t+T)/xt=0.5, e^-bt/2m=50/100, andT=2m/k.

Somehow, I'm not getting the right anwers using these formulas...could someone please show me how to set up my problems to solveparts (a) and (b)? Thank you...

Explanation / Answer

(a)

   to get the force constant of the spring we usethe hookes law so that we get

   k = (500 kg) (9.80 m / s2) / (10cm)

      = N / cm

(b)

   for simplicity let us take the decrease ofamplitude is 50% then we get

   e-b /2 M = 1 / 2 where

   T = 2 / '

    ' =

         = (k /m)

   solve for ' and then for T

   taking the log of both sides of the above equationand rearranging we get that

   b = (2 m / T) ln 2

      = ........... kg / s

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