The problem is as follows:

A mass whose mass is $m$ is hanging vertically from a ceiling which is tied to a spring which has a constant of $K$ is oscillating. Given this condition find the velocity as a function of the elongation of the spring.

The alternatives given are as follows:

$\begin{array}{ll}

1.&\sqrt{\frac{K}{m}y^2+2gy}\\

2.&\sqrt{2gy-\frac{K}{m}y^2}\\

3.&\sqrt{\frac{K}{m}y^2-2gy}\\

4.&\sqrt{\frac{K}{m}y}\\

5.&\sqrt{2gy}\\

\end{array}$

How exactly should I find the velocity in this situation?. Could it be that since appears a square root that is related to the conservation of mechanical energy?

If this is the case it would be that:

$\frac{1}{2}ky^2=\frac{1}{2}mv^2$

Therefore in this situation it would be:

$v=\sqrt{\frac{ky^2}{m}}$

But it doesn't appear in any of the alternatives. Exactly which part did I missunderstood. Can someone help me here?. Upon inspecting this problem it doesn't explicitly mentions anything regarding the height, but I'm assuming that the elongation is $y$ and it might be the intended meaning in this problem. But as indicated it doesn't check with any of the alternatives. Can anyone help me here please?.

A mass whose mass is $m$ is hanging vertically from a ceiling which is tied to a spring which has a constant of $K$ is oscillating. Given this condition find the velocity as a function of the elongation of the spring.

The alternatives given are as follows:

$\begin{array}{ll}

1.&\sqrt{\frac{K}{m}y^2+2gy}\\

2.&\sqrt{2gy-\frac{K}{m}y^2}\\

3.&\sqrt{\frac{K}{m}y^2-2gy}\\

4.&\sqrt{\frac{K}{m}y}\\

5.&\sqrt{2gy}\\

\end{array}$

How exactly should I find the velocity in this situation?. Could it be that since appears a square root that is related to the conservation of mechanical energy?

If this is the case it would be that:

$\frac{1}{2}ky^2=\frac{1}{2}mv^2$

Therefore in this situation it would be:

$v=\sqrt{\frac{ky^2}{m}}$

But it doesn't appear in any of the alternatives. Exactly which part did I missunderstood. Can someone help me here?. Upon inspecting this problem it doesn't explicitly mentions anything regarding the height, but I'm assuming that the elongation is $y$ and it might be the intended meaning in this problem. But as indicated it doesn't check with any of the alternatives. Can anyone help me here please?.

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