Natural frequencies and mode shapes of a full car model. Consider a vehicle with a the following characteristics.

m $=840$ kg

mf $=53$ kg

mr $=76$ kg

Ix $=820$ kg m$^2$

Iy $=1100$ kg m$^2$

a$1=1\mathrm{.}4$ m

a$2=1\mathrm{.}47$ m

b$1=0\mathrm{.}7$ m

b$2=0\mathrm{.}75$ m

kf $=10000$ N$/$ m

kr $=13000$ N$/$ m

ktf $=$ ktr $=200000$ N$/$ m

kR $=10000$ N m$/$ rad

Using the matrix $[$A$]=[$m$]^1[$k$]$ and solving the associated eigenvalue and eigenvector problems, we find the following natural frequencies, and mode shapes for the full car model$\mathrm{.}1-$ Natural frequencies and mode shapes of the full car model by using related commands in MATLAB script file. Plot all mode shapes.

$2-2-$ Suppose that the front left wheel encounters a road bump when the vehicle velocity is $1$ m$/$s$.$ Solve the differential equations for this kind of road excitation and plot all states variation versus time. Use related codes in MATLAB script file. The road bump can be approximated as half circle with $10$ cm radius