We explore the spring-mass oscillator, introducing the restoring force and potential energy. The restoring force, following Hooke's Law, is proportional to displacement and returns the mass to equilib...We explore the spring-mass oscillator, introducing the restoring force and potential energy. The restoring force, following Hooke's Law, is proportional to displacement and returns the mass to equilibrium. Potential energy depends on displacement squared, increasing as the spring stretches or compresses. We explain that vertical spring-mass systems account for gravity if equilibrium is defined with the mass attached, making vertical and horizontal setups behave similarly.