$A$ metal ball released from height $h$ makes a perfectly elastic collision with the ground. The frequency of the periodic vibratory motion is $\quad(g = \text{acceleration due to gravity})$

• A
  $\frac{1}{2} \sqrt{\frac{g}{2 h}}$
• B
  $\frac{1}{2} \sqrt{\frac{2 h}{g}}$
• C
  $\frac{1}{2 \pi} \sqrt{\frac{g}{2 h}}$
• D
  $\frac{1}{2 \pi} \sqrt{\frac{2 h}{g}}$