Using the required parameters for a typical large size car* and an appropriate frontal Quarter-Car model:
a) Approximating the system to a single mass, estimate the sprung and un-sprung mass natural frequencies and suspension damping ratio.
b) Obtain and provide the car's ride equations of motion for the 2 DOF Quarter-Car model. Give your answer in Matrix form in terms of variables including damping.
c) Obtain the natural frequencies and mode shapes, using equations in (b).
d) Repeat (c) using Eigen-value solution using the M and K matrices for the system. (Give the M and K matrices and Eigen-value solutions using Matlab or other tool and interpret the results).
e) Compare and comment on the results obtained in (a), (c) and (d).
f) Obtain the expressions for displacement transmissibility of sprung and unsprung masses.
g) Obtain the plots for (f) using tool of your choice for baseline parameters and for twice the damping ratio.