Describe energy transformations in a oscillating pendulum, which undergoes simple harmonic motion. How this implies the velocity at critical (lowest and highest) points?

Our object will have a combination of potential energy (due to it's position relative to the ground) and kinetic energy (due to it's velocity).Consider the potential energy first. It depends on the height of the pendulum, it's mass and the gravitational acceleration (E_p = mgh), so it will have a zero value at the lowest point (as h=0), and the maximum value at the highest points (other terms are constants). Recall the law of conservation of energy: energy can be transformed from potential to kinetic and vise versa, but the total energy always stays the same. So the kinetic energy is minimum at the highest points and maximum at the lowest point of oscillation. In general, as the pendulum goes through a half cycle starting from equilibrium position, energy is transferred from kinetic, to potential, and then back to kinetic. As kinetic energy is directly proportional to the square of velocity of an object (E_k=0.5mv²), it will therefore have maximum velocity at it's lowest point and velocity will be zero at the highest points. (More detailed analysis can be done by considering restoring force and drawing energy against displacement graphs.)