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 0.15 m when the entire automobile is placed on it. Also, the amplitude of oscillation decreases by `50%` during one complete oscillation. Estimate the value of (a) the spring constant k and (b) damping constant'b' for the spring and shock absorber system of one wheel, assuming that each wheel supports 750 kg `(g=10ms^(-2)).`

Explanation

Given, `M=3000kg" "m=750kg`
Since the weight is supported on 4 shocks
`Mg=-4ky`
hence spring constant `k=(3000xx10)/(4xx0.15)`
`"i.e. "k=5xx10^(4)Nm^(-1)`
(b) Mass supported by each spring `=(3000)/(4)=750kg`
using`" "y=Ae^(-bt//2m) and t=T" "y=(A)/(2)and log_(e)=2=0.693`
`"or "(bt)/(2m)=0.693" or "b=(2xx750xx0.693)/(T)`
`"i.e. "b=(1039.5)/(T)`
`"where "T=2pisqrt((M)/(4k))=2xx3.142xxsqrt((3000)/(4xx5xx10^(4)))`
`"i.e. "T=0.7698s`
`"hence "b=(1039.5)/(0.768)`
`b=1.350xx10^(3)" kgs"^(-1).`