The average kinetic energy during its motion from the position of equilibrium to the end will be given by:
=∫T/4012mV2T/4
Substitute V=aωcosωt
K.Eavg=∫T/4012m(aωcosωt)2T/4
After solving,
K.Eavg=14ma2ω2
Now, substitute ω=2πv
K.Eavg=14ma2(2πv)2
K.Eavg=π2ma2v2