You should be well-grounded in the basics of energy. Here is all the theory you are responsible for at this point:
What is work? The cosine term in the equation is not strictly necessary as long as you understand the force to be in the direction of motion.
Gravitational potential energy:
Elastic potential energy: (from a compressed spring)
Energy is conserved:
Please note that his approach to energy problems involves a LOT of writing as all forms of energy – even ones that don’t exist at a given time – are written out. We won’t usually do this in class but focus on the CHANGE in energy.