## College Physics (4th Edition)

We can rank the systems in decreasing order of their total energy: $c \gt a = b \gt d = e$
$E = \frac{1}{2}kA^2$, where $k$ is the spring constant and $A$ is the amplitude. We can use the spring constant and the amplitude to find the total energy in each system: (a) $E = \frac{1}{2}kA^2$ (b) $E = \frac{1}{2}kA^2$ (c) $E = \frac{1}{2}k(2A)^2 = 4\times \frac{1}{2}kA^2$ (d) $E = \frac{1}{2}(k/2)A^2 = \frac{1}{2}\times \frac{1}{2}kA^2$ (e) $E = \frac{1}{2}(2k)(A/2)^2 = \frac{1}{2}\times \frac{1}{2}kA^2$ We can rank the systems in decreasing order of their total energy: $c \gt a = b \gt d = e$