POTENTIAL ENERGY AND KINETIC ENERGY

One of the most fundamental forms of energy is the position of a mass within a gravitational field near the earth's surface. The gravitational potential energy  is defined as the constant weight  moved against a constant gravitational field of distance  . Or:

A mass that is moving with velocity  has kinetic energy given by the following equation:

One of the most common examples that illustrates the physical significance of both the potential and kinetic energy is the behavior of a pendulum.

If the mass of the pendulum has an initial position of  , the kinetic energy is zero and the potential energy is  . When  equals zero, the potential energy is zero; therefore, from conservation of energy, the kinetic energy is:

Reference

Three-Dimensional Static and Dynamic Analysis of Structures A Physical Approach With Emphasis on Earthquake Engineering Edward L. Wilson