Simple Harmonic Motion: Finding the Phase Constant

Abstract

The treatment of mechanical oscillations in General Physics courses usually begins with the study of Simple Harmonic Motion in a system composed of a block attached to the end of a spring. To obtain the law of motion for such system involves finding the phase constant as a difficult step for students. To determine the phase constant requires operating with two independent equations related with the particle’s initial speed and position. Some textbooks oversimplify the procedure and obtain the phase constant using only one equation related to the initial conditions of the motion. How to determine the phase constant for such oscillatory systems is discussed.