I know how to arrive at a = -(k/m)x for a SHM system. However, most derivations i found did an unexplained step from here onward. They simply let k/m = ω2. And later on then mention ω as the angular frequency and link to the period of oscillation. My question is, Why did that substitution take place? Why must it be ω2? Why can't k/m = v3 or anything else? Please help as I couldn't find any explanation for this step!