For a particle executing simple harmonic motion,  the kinetic energy K is given by, K0cos2⁡ωt. The maximum value of PE is

KE =K0 cos2ωt we know KE=12m(Aω cosωt)2 ; if displacement y=Asinωt maximum KE =K0=12m(Aω)2 PE=12mω2(Asinωt)2 maximum PE=12m(Aω)2=K0 for maximum value of PE or KE , sinωt=1=cosωtThe mechanical energy of a simple harmonic motion is conserved. Since K = K0  cos2ωt, the maximum value of Kinetic energy = K0 = maximum value of potential  energy at the extreme position of the body in simple harmonic motion.