### 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