Question

What is effective mass of the spring?

Answer 1

1. The effective mass of a spring in a spring-mass system, when using an ideal spring with uniform linear density, is one-third of the mass of the spring and is not dependent on the direction of the spring-mass system (i.e., horizontal, vertical, and oblique systems all have the same effective mass).
2. This is due to the fact that external acceleration has no effect on the period of motion around the equilibrium point.
3. The spring's effective mass can be determined using its kinetic energy.
4. The effective mass is a quantity used to simplify band structures by modeling the behavior of a free particle with that mass.
5. The effective mass of the spring along its length is equal to $\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$3$}\right.$ rd of its actual mass.
6. The period of oscillation is affected by the mass of the spring.
   $T=2\pi \sqrt{\frac{m}{k}}$
   it also rewritten as $T=2\pi \sqrt{\frac{m+m_s}{k}}$
   where $m_s$is the effective mass of the spring.