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In general we have the energy relationship


where $K$ is the kinetic, $U$ the potential, and $E$ the total energy. Kinetic energy is always non-negative ($K \propto v^2$), and for a spring so too is the potential ($U \propto x^2$).

Thus, if we set $K=0$ we get


while if we set $U=0$ we get


Solving the first eqation for $k$ yeilds


and solving the second for $m$ yields


Dan Cross 2006-10-18