SHM is a special type of periodic motion where the restoring force on a moving object is porportional to the object's displacement magnitude. Please note that derivations of SHM equations are not usually required within your exams, however, derivations using calculus are included for your interest.
There are two main harmonic systems: The Mass Spring System and the Simple Pendulum.
The total energy of a simple harmonic system is always constant as it is the sum of the kinetic and potential energies of the system. Disspiative forces can dampen the motion of a harmonic motion.
A system is in reasonance when the periodic force is in phase with the velocity of the oscillating system. The lighter the damping, the larger the max amplitude at reasonance and the closer resonant frequency is to the natural frequency.