( A ) a periodic, but not simple harmonic, motion with a period $\frac{\pi}{\omega}$
( B ) a periodic, but not simple harmonic, motion with a period $\frac{2\pi}{\omega}$
( C ) a simple harmonic motion with a period $\frac{2 \pi}{\omega}$
( D ) a simple harmonic motion with a period $\frac{\pi}{\omega}$
