$A$ trolley of mass $m_1$ is placed on a horizontal rigid pair of rails at the same height. $A$ mass $m_2$ is suspended from the trolley vertically by means of an ideal massless rope. The rope hangs between the rails without touching them. The trolley can move along smooth rails but cannot move in any other direction. The suspended mass is given a small oscillation and performs $SHM$ after being displaced slightly from its stable equilibrium position in two ways: first,perpendicular to the rails,and second,parallel to the rails. The ratio of the time periods of these two $SHM$s (second case to first case) is:

• A
  $\sqrt{\frac{m_1}{m_1 + m_2}}$
• B
  $\sqrt{\frac{m_2}{m_1 + m_2}}$
• C
  $\sqrt{\frac{m_1}{m_2}}$
• D
  $\sqrt{\frac{m_2}{m_1}}$