Final answer:
The equation of motion for a damped pendulum is ml^2θ¨ + bθ˙ + mglsinθ = 0. We can analyze the stability of the equilibrium using the linearization method. In the absence of friction, the equation simplifies to ml^2θ¨ + mglsinθ = 0.
Step-by-step explanation:
The simple pendulum is a nonlinear time-invariant dynamical system. The equation of motion for a damped pendulum is given by ml^2θ¨ + bθ˙ + mglsinθ = 0. (a) To analyze the stability of the equilibrium, we can use the linearization method for stability analysis. (b) In the absence of friction (b=0), the equation becomes ml^2θ¨ + mglsinθ = 0.