You are riding in an automobile of mass 3000 kg. Assuming that you are examining the oscillation characteristics of its suspension system. The suspension sags 15 cm when the entire automobile is placed on it. Also, the amplitude of oscillation decreases by 50% during one complete oscillation. Estimate the values of the damping constant b for the spring and shock absorbar system of one wheel, assuming that each wheel supports 750 kg.

Explanation

For each spring system supporting 750 kg of weight.
Time period `T= 2pi sqrt((m)/(k))`
`= 2xx 3.14 xx sqrt((750)/(5xx 10^4))`
`= 6.28 xx sqrt(150 xx 10^(-4))`
`= 6.28 xx sqrt(0.015) = 6.28xx 0.122`
`= 0.769 approx 0.77s`.
Now displacement of damped oscillation at time t,
`x= x_(0) e^(-(bt)/(2m))`
`therefore (x_0)/(2) = x_(0) e^(-(bt)/(2m))`
`therefore 2= e^((bt)/(2m))`
`therefore ln2 = (bt)/(2m)" "[therefore " Taking log on both side "]`
`2.303 log 2 = (bt)/(2m)`
`therefore 2.303 xx 0.3010 = (bt)/(2m)`
`therefore (0.693 xx 2m)/(t) =b`
`therefore b = (0.693xx 2 xx 750)/(0.77)`
`therefore b = 1350 kg s^(-1)`.