### Kinetic Energy of a Mass

*Kinetic energy*is energy associated with

*motion*. For example, when a spring uncompresses and accelerates a mass, as in the configuration of Fig.B.2, work is performed on the mass by the spring, and we say that the potential energy of the spring is converted to

*kinetic energy*of the mass.

Suppose in Fig.B.2 we have an initial spring compression by meters at time , and the mass velocity is zero at . Then from the equation of motion Eq.(B.5), we can calculate when the spring returns to rest (). This first happens at the first zero of , which is time . At this time, the velocity, given by the time-derivative of Eq.(B.5),

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Mass Kinetic Energy from Virtual Work

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Potential Energy in a Spring