$$ $$ $$ $$ $$ $$ $$ $$ $$ $\text{Extra close brace or missing open brace}$ $\text{Extra close brace or missing open brace}$ $$

Energy of a Block on a Spring

For an undamped block-spring oscillator, the total energy remains constant throughout and is equal to $$E_{tot}=\frac{1}{2}k{A}^2+\frac{1}{2}m{v}_{max}^2$$ This energy moves back and forth between the kinetic and spring potential energies: $$\begin{array}{rl}{E}_{tot}& =E_k+E_s\\ & =\frac{1}{2}m(v(t){)}^2+\frac{1}{2}k(y(t){)}^2\end{array}$$ where $y(t)$ is the displacement of the block, and $v(t)$ the velocity, at a given time $t$.