How to prepare the inverted pendulum with a moving vertically base in Mathematica?

(a) Prepare the Mathematica model of the inverted pendulum with a moving vertically base (1): i. define a function which returns the pendulum base position, ii. define a function which returns the mass m position, iii. define the differential equation 1. Analyze the model behavior for an initial value equal to 0 and 0.2, and the steady base (y=0). Plot the joint angle as a function of time. Animate the pendulum movement. Investigate the influence of the dumping coefficient on the pendulum behavior.