A forcing force acts on the system in the figure by means of an unbalanced rotating disk. In the case of permanent vibration, e is the eccentricity, M is the system mass, m is the unbalanced mass, k is the spring constant and c is the damping coefficient. In the supra$-$resonant region of the system and $/=1\mathrm{.}36.$

e$=0\mathrm{.}15[$m$],$ M$=40[$kg$],$ m$=0\mathrm{.}4[$kg$],$ n$=1250[$rpm$]$

a$)$ In the case where $\backslash$xi $=0$; the system

$-$ Find the natural frequency.

$-$ Calculate the coefficient of damping and spring element.

$-$ Write the differential equation.

$-$ Find the equation of motion and plot it in Matlab for $5$ s$.$

b$)$ In case $\backslash$xi $=0\mathrm{.}35$; the system

$-$ Find the natural frequency with and without damping.

$-$ Calculate the coefficient of damping and spring element.

$-$ Write the differential equation.

$-$ Find the equation of motion and plot it in Matlab for $5$ s$.$