A block of mass $m=8.0\ \mathrm{kg}$ is attached to an ideal spring of force constant $k=500\ \mathrm{\displaystyle \frac{N}{m}}$. The block is at rest at its equilibrium position. An impulsive force acts on the block, giving it an initial speed of $k=2.0\ \mathrm{\displaystyle \frac{m}{s}}$.
Find the amplitude of the resulting oscillations.
$A=0.25\ \mathrm{m}$
The block will come to rest when all of its initial kinetic energy has been transformed into the spring’s potential energy. At this point, the block is at its maximum displacement from equilibrium, at one of its amplitude positions, and
$$K_{\mathrm{i}}+ U_{\mathrm{i}}=K_{\mathrm{ff}}+U$$
$$\frac{1}{2}mv^2_i+0=0+\frac{1}{2}kA^2$$
$$A=\sqrt{\frac{mv^2_i}{k}}$$
$$A=\sqrt{\frac{(8.0\ \mathrm{kg})\left(2.0\ \mathrm{\displaystyle \frac{m}{s}}\right)^2}{500\ \mathrm{\displaystyle \frac{N}{m}}}}$$
$$A=0.25\ \mathrm{m}$$