DOING PHYSICS WITH MATLAB MECHANICS   VIBRATION OF A SPRING       CONSERVATION OF ENERGY Ian Cooper School of Physics, University of Sydney ian.cooper@sydney.edu.au DOWNLOAD DIRECTORY FOR MATLAB SCRIPTS mec_spring_energy.m The mscript is used to create an animated gif of a vibrating spring. The animation shows the spring, and the time evolution of the kinetic energy of the object; the potential energy of the system and the total energy of the system. Energy in Simple Harmonic Motion Consider a system of an object of mass m vibrating at the end of a spring with a spring constant k. Ignoring any frictional effects, the total energy E of the system is conserved. The kinetic energy EK of the object is and the potential energy EP of the system is Total energy E of the system is At the equilibrium position, x = 0, the objects moves with its maximum speed vmax and its kinetic energy is a maximum  and the potential energy of the system is zero . At the points of extreme motion, the amplitude of the motion is x = ± A = ± xmax, the kinetic energy of the object is zero  and the potential energy of the system has its maximum value . Therefore, we can write the statement of conservation of energy as The kinetic energy EK and potential energy EP vary with time while the total energy E is time independent. The animated gif shows the time evolution of the energies. The animated gif was created with the mscript mec_spring_energy.m.