A time series of free decay of an automobile suspension syst

A time series of free decay of an automobile suspension system is shown below. A suspension system can be modeled as a single degree of freedom mass-spring-damper system. The vertical displacement is given in meters and the time is given in seconds. From the figure, determine the natural frequency w_ n the damping ratio epsilon, and the damped natural frequency w_ d.

Solution

Logarithmic decrement,m : ln (x1/x2) = ln (0.5/0.075) = 1.89711
now, damping ratio, z = m/sqroot([2*pi]^2 + m^2) = 1.89711/sqroot((2pi)^2 + (1.89)^2) = 0.2891

damped angular frequency,Wd = 2pi/T = 25.12 ( T = 0.25 from graph)
natural frequenct, Wn = Wd/sqroot(1-z^2) = 26.24