A mass $m_1=1 \mathrm{kg}$ connected to a horizontal spring performs S.H.M. with amplitude $A$. While mass $m_1$ is passing through mean position another mass $m_2=3 \mathrm{kg}$ is placed on it so that both the masses move together with amplitude $A_1$. The ratio of $\frac{A_1}{A}$ is ${\left(\frac{p}{q}\right)}^{\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$2$}\right.}$, where $p$ and $q$ are the smallest integers. Then what is the value of $p+q$?

Hence, the correct answer is 5.