I'm struggling to understand concepts involving potential energy and kinetic energy. Could someone briefly explain these energies in terms of particles dangling from elastic strings. If potential energy is stored energy why has my tutor given me the equations

potential energy = mgh

stored energy = $\displaystyle \frac{1}{2}\frac{\lambda x^2}{l}$

Also before i delve into simple harmonic motion, is it true to say SHM is sort of an extension of hooke's law?