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Question
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 absorber system of one wheel, assuming that each wheel supports 750 kg.
Solution
For each spring system supporing 750 kg of weight
`"t" = 2 pi sqrt("m"/"k")`
`= 2 xx 3.14 xx sqrt(750/(5xx10^4))`
= 0.77 sec
`therefore "Using" x = x_0 "e"^(-("bt")/("2m"))` we get
`50/100 x_0 = x_0 e^-(bxx0.77)/(2xx750)` or `e^((0.77b)/1500) = 2`
Taking logarithm of both sides
`(0.77b)/1500 = ln 2 = 2.303 log 2`
`:. "b" = 1500/0.77 xx 2.303 xx 0.3010`
`= 1350.4 "kg s"^(-1)`
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