Question $2-$ subject name is dynamics of mechanical systems

A homogeneous pendulum rod of mass is install in the elevator car shown in thefigure $2,$ the gravity $g=10\frac{m}{s^2},$ and the acceleration is $a.$

Try:

$(1)$ to establish the differential equation of motion with the swing angle $$;

$(2)$ if the swing of the pendulum is very small, namely $sin$~~$,$ simplify the differential equation of motion and calculate its natural frequency. ${}_n($Note: if to calculate ${}_n,$ values of $m,k,a,b,l$ equal to $4).$