A new approach to the study of simple harmonic motion is presented. A record is taken of the positions at different times by means of a spark timer. From the limits approached by the average velocities, instantaneous velocities are obtained. From the limits approached by the average accelerations, instantaneous accelerations are obtained. A linear relation shows the direct proportionality between acceleration and displacement. The period of SHM may be determined from the slope of this straight line and compared with the experimental value.