Question

At what distance from the mean position, is the K.E. in S.H. oscillation equal to P.E.?

Answer 1

When the displacement of a particle executing S.H.M. is y, then its

K.E. = 1/2 mω² (a² - y²)

and P.E. = 1/2 mω²y²

If K.E. = P.E., then

1/2mω² (a² - y²) = 1/2 mω² y²

or, 2y² = a²

or, y = a√2