In the inverted pendulum system shown below,

Assume that the mass of the inverted pendulum is $m$ and that the mass is evenly distributed along the length of the rod $($The center of mass of the pendulum is located at the midpoint of the rod.$)$

a$)$ Write the equations of motion for the system using differential equations in the appropriate form, reading the comments in the code lines correctly.

b$)$ Find the transfer function $\frac{(s)}{U(s)}$ using the equation you obtained.

c$)M=0\mathrm{.}7kg,m=0\mathrm{.}3kg,l=0\mathrm{.}4m,I=0\mathrm{.}008kg*m^2$ rewrite the transfer function using the numerical values $($First use the subs$()$ then the MATLAB $)$ commands, detailed information has been provided in the code comment lines$).$