$A$ mass '$m_1$' is suspended from a spring of negligible mass. The spring is pulled slightly in the downward direction and released; the mass performs $S.H.M.$ with a period '$T_1$'. If the mass is increased by '$m_2$',the time period becomes '$T_2$'. The ratio $\frac{m_2}{m_1}$ is

• A
  $\frac{T_1^2+T_2^2}{T_1^2}$
• B
  $\frac{T_1-T_2}{T_1}$
• C
  $\frac{T_2^2-T_1^2}{T_1^2}$
• D
  $\frac{T_1^2-T_2^2}{T_1^2}$