The mechanical energy of the block at position \(A\) is thus: \[\begin{aligned} K_A&=0\\ U_A&=\frac{1}{2}kD^2\\ \therefore E_A &= U_A + K_A = \frac{1}{2}kD^2\end{aligned}\] At position \(B\), the spri...The mechanical energy of the block at position \(A\) is thus: \[\begin{aligned} K_A&=0\\ U_A&=\frac{1}{2}kD^2\\ \therefore E_A &= U_A + K_A = \frac{1}{2}kD^2\end{aligned}\] At position \(B\), the spring potential energy of the block is zero (since the spring is at rest), and all of the energy is kinetic: \[\begin{aligned} K_B&=\frac{1}{2}mv_B^2\\ U_B&=0\\ \therefore E_B &= U_B+K_B=\frac{1}{2}mv_B^2\end{aligned}\] Since there are no non-conservative forces doing work on the block, the mechanical…
