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 15cm when the entire automobile is placed on it. Also, the amplitude of oscillation decreases by 50% during one complete oscillation. Estimate the values of (a) the spring constant k and (b) the damping constant b for the spring and shock absorber system of one wheel, assuming that each wheel supports 750 kg.

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 15cm when the entire automobile is placed on it. Also, the amplitude of oscillation decreases by 50% during one complete oscillation. Estimate the values of (a) the spring constant k and (b) the damping constant b for the spring and shock absorber system of one wheel, assuming that each wheel supports 750 kg.
Answer» SOLUTION :`F= mg = 3000 xx 10 = 3 xx 10^(4) N. X =-15 x× 10^(-2) m` 4 springs in parallel K=4K, F=-(4K) x. `K= -(F)/(4x)= (-3 xx 10^(4))/(4(-15xx 10^(2)))= 5 xx 10^(4) N//m` b) mass supported by each spring`m = (3000)/(4)= 750 Kg` damped oscillations amplitude `A_(t)= Ae^(-bt//2m)` time period `T= 2pisqrt((m)/(K))= 2 xx 3.14 sqrt((750)/( 5XX 10^(4)))= 77xx 10^(-2) "seconds"` Amplitude decreases by 50% then `At =A//2` and t = T `:. (A)/(2)= Ae^(-bt//2m)` or `b= (0.693 xx 2m)/(T)` `b= 1350 kg//s`