A particle of mass \(m\) oscillates with simple harmonic motion (SHM) of angular frequency \(\omega \). The amplitude of the SHM is \(A\). What is the kinetic energy of the particle when it is half way between the equilibrium position and one extreme of the motion?

A.     \(\frac{{m{A^2}{\omega ^2}}}{4}\)

B.     \(\frac{{3m{A^2}{\omega ^2}}}{8}\)

C.     \(\frac{{9m{A^2}{\omega ^2}}}{{32}}\)

D.     \(\frac{{15m{A^2}{\omega ^2}}}{{32}}\)

B