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Mass spring system
In a real spring–mass system, the spring has a non-negligible mass
m
{\displaystyle m}
. Since not all of the spring's length moves at the same velocity
v
{\displaystyle v}
as the suspended mass
M
{\displaystyle M}
, its kinetic energy is not equal to
1
2
m
v
2
{\displaystyle {\tfrac {1}{2}}mv^{2}}
. As such,
m
{\displaystyle m}
cannot be simply added to
M
{\displaystyle M}
to determine the frequency of oscillation, and the effective mass of the spring is defined as the mass that needs to be added to
M
{\displaystyle M}
to correctly predict the behavior of the system.
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