SE ENCUENTRA UNA FAMILIA DE LAGRANGIANOS Y HAMILTONIANOS NO EQUIVALENTES DEL OSCILADOR ARMÓNICO EN UNA DIMENSIÓN. ESTOS LAGRANGIANOS SON DEDUCIDOS UTILIZANDO EL PROCEDIMIENTO DE ENCONTRAR INICIALMENTE UNA CONSTANTE DE MOVIMIENTO DEL SISTEMA. EL ESTUDIO SE CENTRA EN UNO DE ESTOS LAGRANGIANOS Y SU CORRESPONDIENTE HAMILTONIANO PARA ANALIZAR SUS IMPLICACIONES EN LA CUANTIZACIÓN DEL OSCILADOR ARMÓNICO UNIDIMENSIONAL. EL RESULTADO FUNDAMENTAL ES LA INCOMPATIBILIDAD EN EL SISTEMA DE UNIDADES EN LA CUANTIZACIÓN NORMAL. USANDO LA CUANTIZACIÓN DE LA VELOCIDAD, ES POSIBLE HACER A UN LADO ESTE PROBLEMA DE INCOMPATIBILIDAD DE LAS UNIDADES.AbstractA FAMILY OF NONEQUIVALENTS LAGRANGIANS AND HAMILTONIANS ARE GIVEN FOR THE ONE-DIMENSIONAL HARMONIC OSCILLATOR. THESE LAGRANGIANS ARE DEDUCED USING THE CONSTANT OF MOTION APPROACH. THE STUDY IS FOCUSED ON ONE OF THESE LAGRANGIANS AND HAMILTONIANS TO ANALYZE THEIR IMPLICATIONS ON THE QUANTIZATION OF THE ONE-DIMENSIONAL HARMONIC OSCILLATOR. THE MAIN FEATURE IS THE INCOMPATIBILITIES OF THE UNITS IN THE USUAL QUANTIZATION APPROACHES. USING THE VELOCITY QUANTIZATION APPROACH IT IS POSSIBLE TO GET RID OF THIS INCOMPATIBILITY UNITS PROBLEM.A FAMILY OF NONEQUIVALENTS LAGRANGIANS AND HAMILTONIANS ARE GIVEN FOR THE ONE-DIMENSIONAL HARMONIC OSCILLATOR. THESE LAGRANGIANS ARE DEDUCED USING THE CONSTANT OF MOTION APPROACH. THE STUDY IS FOCUSED ON ONE OF THESE LAGRANGIANS AND HAMILTONIANS TO ANALYZE THEIR IMPLICATIONS ON THE QUANTIZATION OF THE ONE-DIMENSIONAL HARMONIC OSCILLATOR. THE MAIN FEATURE IS THE INCOMPATIBILITIES OF THE UNITS IN THE USUAL QUANTIZATION APPROACHES. USING THE VELOCITY QUANTIZATION APPROACH IT IS POSSIBLE TO GET RID OF THIS INCOMPATIBILITY UNITS PROBLEM.