Answer:
If x = A sin w t where w is the angular frequency
then v = w A cos w t
Since KE = 1/2 m Vmax^2 and Vmax = w A maximum KE
the total energy is proportional to A^2
Also, since the maximum potential energy is
PEmax = 1/2 K A^2 where the KE is zero (maximum amplitude)
one can again see that the total energy is proportional to A^2
