You are riding in an automobile of mass 3000 kg . Assuming that you are examining the oscillation characterisitics 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 value of the damping constant b for the spring and shock absorbed system of one wheel, assuming that each wheel supports 750 kg. g= 10 m//s^2

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

1.	You are riding in an automobile of mass 3000 kg . Assuming that you are examining the oscillation characterisitics 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 value of the damping constant b for the spring and shock absorbed system of one wheel, assuming that each wheel supports 750 kg. g= 10 m//s^2
Answer» Solution :If m is the mass SUPPORTED by each spring , then `m =(3000)/4 = 750 KG` `X= x_0 e^(-bt//2m) ` or `2 = e^(bt//2m)` or `log_e 2 =(bt)/(2m) log_e e = (bt)/(2m)` where `t= 2pi sqrt(M/K) = 2 xx (22)/(7) xx sqrt((3000)/(4 xx 5 xx 10^4)) = (44)/(70) sqrt(3/2)` `therefore b= (2m log_e 2)/(t) = (2xx 750 xx 0.6931)/((44)/(70) sqrt(3/2)) = 1350.4 ` kg/s