I have a question about a problem I saw on a website
A mass is attached to one end of a spring, and the other end of the spring is attached to an immovable wall. The system oscillates with period T. If the wall is removed and replaced with a second mass identical to the first, what is the new period of oscillation of the system?
My answer: $\frac{T}{\sqrt{2}}$
Website's answer (Incorrect thanks to trula): $T\sqrt{2}$
My thought process (pretty hand-wavy I know):
Because the spring constant is inversely proportional (I think) to length of the spring, the spring constant will be doubled if you halve the length of the spring, which is what is essentially happening with two identical massess. Because $T=2\pi\sqrt{\frac{m}{k}}$, if you double $k$, you divide $T$ by $\sqrt{2}$. I don't know why they got $T\sqrt{2}$, but if I am wrong, please correct my misunderstandings.
Thanks for reading if you made it this far, and if my question is unclear, please tell me what I can fix about it.