10.2 Energy Considerations

A mass and spring make a prototype simple harmonic oscillator. The mass sits on a horizontal, frictionless surface like an air track.

When it passes through equilibrium it moves with its maximum speed, vmax. That means it has maximum kinetic energy at that position.

As it continues, the spring exerts a force on the mass which does work on it and slows it down. When the displacement is at its maximum-called the amplitude-the mass momentarily stops and its kinetic energy at that point is zero. While the spring has been doing work on the mass it has also been storing elastic potential energy. When the mass has stopped and the kinetic energy is zero, the potential energy of the spring is maximum.

At the equilibrium position, where the kinetic energy was maximum, the potential energy was zero.

The amount of kinetic energy and the amount of potential energy vary but their sum-the total energy of the oscillator-remains constant throughout the motion. This is another example of energy conservation.

Figure 10.5 As a mass and spring-which form a simple harmonic oscillator -move through a cycle, the total amount of energy remains constant but changes from kinetic energy to potential energy and back to kinetic energy again.

The same ideas apply for a simple pendulum, another example of a simple harmonic oscillator. As the pendulum passes through its equilibrium position, it is at its lowest position and has zero gravitational potential energy. At that position it moves fastest and has maximum kinetic energy.

As it continues its swing, it rises higher, increasing its potential energy. As it continues its swing, it slows down, decreasing its kinetic energy.

The amount of kinetic energy and the amount of potential energy vary but their sum-the total energy of the oscillator-remains constant throughout the motion. This is yet another example of energy conservation.

Figure 10.6 As a pendulum-another simple harmonic oscillator-moves through its cycle, the total amount of energy remains constant but changes from kinetic energy to potential energy and back to kinetic energy again.