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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
At the points of extreme motion, the
amplitude of the motion is x = ± A = ± xmax, the kinetic energy of the object is zero
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.
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