When the displacement of a mass on a spring is 12a the half of the amplitude, what fraction of the mechanical energy is kinetic energy? at what displacement, as a fraction of a, is the mechanical energy half kinetic and half potential?

As the object displacement is half of the amplitude then the potential energy stored in the spring is given by

here we know that

total mechanical energy is given as

now KE is given by

now fraction of KE with respect to ME is given as

now if the mechanical energy is divided equally in KE and PE

so now we will have

now we have