Answer
We can rank the systems in decreasing order of their total energy:
$c \gt a = b \gt d = e$
Work Step by Step
$E = \frac{1}{2}kA^2$, 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:
$c \gt a = b \gt d = e$
