English: A mass ${\displaystyle {\color {Red}m}}$ is attached to a spring of length ${\displaystyle r}$. The opposite end of the spring is attached to the point O. The mass has been displaced from its equilibrium point by ${\displaystyle \xi }$ in the ${\displaystyle {\hat {x}}}$ direction and by ${\displaystyle \eta }$ in the ${\displaystyle {\hat {y}}}$ direction (both ${\displaystyle \xi }$ and ${\displaystyle \eta }$ are assumed small for a wave in the linear regime.) The vector ${\displaystyle {\vec {\ell }}}$ represents the distance between consecutive lumped masses when the wave amplitude is zero. It is assumed that ${\displaystyle \ell >a}$ because the string is under tension, and ${\displaystyle a}$ is the length of the relaxed spring of spring constant ${\displaystyle \kappa _{s}}$. In expressing Newton's second law, the acceleration is written as ${\displaystyle {\ddot {\vec {r}}}}$ using the convention that a dot denotes differentiation with respect to time.