Value of P.E and K.E

Question

Why in shm for a complete  cycle average  value of k.e and p.e are equal?

Answer 1

The average value of P.E. for complete cycle is given by

The average value of K.E. for complete cycle

Thus average values of K.E. and P.E. of harmonic oscillator are equal and each equal to half of the total energy

K_average = U_average