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The time dependent $2$-periodic system \begin{equation*} \dot x{(t)} = A(t)x{(t)} , \ t\in \mathbb{R}, \ \ x(t) \in\mathbb{C}^{n}\tag{A(t)} \end{equation*} is uniformly exponentially stable if and only if for each real number $\mu$ and each $2$-periodic, $\mathbb{C}^{n}$-valued function $f,$ the solution of the Cauchy Problem \begin{equation*} \left\{\begin{split} \dot y{(t)} &= A(t) y{(t)} + e^{i \mu t}f(t),\ \ t\in \mathbb{R}_+, \ y(t) \in \mathbb{C}^{n} \\ y(0) &= 0 \end{split}\right. \end{equation*} is bounded. In this note we prove a result that has the above result as an immediate corollary. Some new characterizations for uniform exponential stability of $(A(t))$ in terms of the Datko type theorems are also obtained as corollaries.