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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