Always verify dimensions: $[T] = [m/k]^{1/2}$ has units of $\sqrt{\text{kg}/(\text{N/m})} = \sqrt{\text{kg} \cdot \text{m}/\text{N}} = \sqrt{\text{s}^2} = \text{s}$. For energy: $[kA^2] = (\text{N/m})\text{m}^2 = \text{N} \cdot \text{m} = \text{J}$. For velocity: $[\omega A] = (\text{rad/s})(\text{m}) = \text{m/s}$. If your answer has wrong dimensions, it is certainly wrong. This is the fastest error-checking method during the exam.