$A$ simple pendulum of length $L$ is constructed from a point object of mass $m$ suspended by a massless string attached to a fixed pivot point. $A$ small peg is placed at a distance $2L/3$ directly below the fixed pivot point so that the pendulum would swing as shown in the figure. The mass is displaced $5$ degrees from the vertical and released. How long does it take to return to its starting position?

• A
  $\pi\sqrt{\frac{L}{g}} \left(1 + \sqrt{\frac{2}{3}}\right)$
• B
  $\pi \sqrt{\frac{L}{g}} \left(2 + \sqrt{\frac{2}{3}}\right)$
• C
  $\pi \sqrt{\frac{L}{g}} \left(1 + \frac{1}{3}\right)$
• D
  $\pi \sqrt{\frac{L}{g}} \left(1 + \frac{1}{\sqrt{3}}\right)$