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)).

You are riding in an automobile of mass 3000 kg. Assuming that you are

1.	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)).
Answer» SOLUTION :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).`