Effective Mass (spring-mass System)
Effective mass may refer to: * Effective mass (solid-state physics), a property of an excitation in a crystal analogous to the mass of a free particle *Effective mass (spring–mass system) See also *Reduced mass In physics, the reduced mass is the "effective" inertial mass appearing in the two-body problem of Newtonian mechanics. It is a quantity which allows the two-body problem to be solved as if it were a one-body problem. Note, however, that the mass ...

Effective Mass (solid-state Physics)
In solid state physics, a particle's effective mass (often denoted m^*) is the mass that it ''seems'' to have when responding to forces, or the mass that it seems to have when interacting with other identical particles in a thermal distribution. One of the results from the band theory of solids is that the movement of particles in a periodic potential, over long distances larger than the lattice spacing, can be very different from their motion in a vacuum. The effective mass is a quantity that is used to simplify band structures by modeling the behavior of a free particle with that mass. For some purposes and some materials, the effective mass can be considered to be a simple constant of a material. In general, however, the value of effective mass depends on the purpose for which it is used, and can vary depending on a number of factors. For electrons or electron holes in a solid, the effective mass is usually stated as a factor multiplying the rest mass of an electron, ''m'' ...
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Effective Mass (spring–mass System)
In a real spring–mass system, the spring has a non-negligible mass m. Since not all of the spring's length moves at the same velocity v as the suspended mass M, its kinetic energy is not equal to \tfrac m v^2. As such, m cannot be simply added to 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 to correctly predict the behavior of the system. Ideal uniform spring The effective mass of the spring in a spring-mass system when using an ideal spring of uniform linear density is 1/3 of the mass of the spring and is independent of the direction of the spring-mass system (i.e., horizontal, vertical, and oblique systems all have the same effective mass). This is because external acceleration does not affect the period of motion around the equilibrium point. The effective mass of the spring can be determined by finding its kinetic energy. This requires adding all the mass elements' kinetic energy, and r ...
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