The suspension system of a 2100 kg automobile sags 12 cm when the chassis is placed on it. Also, the oscillation amplitude decreases by 54% each cycle. 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 each wheel supports 525 kg.
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For damped oscillations we have x A*e^((-b/2m)*t)*cos(ωd*t + Φ) Now using Hooke's Law k F/x m*g/x 525kg*9.8m/s^2/0.12m 4.29x10^4N/m The damping is 0.46 e^(-b/(2m*sqrt(k/m))) so b -ln(0.46)*2*525*sqrt(4.29x10^4/525) 7370 kg/s
