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Two springs, each with spring constant $k$ and relaxed length $l$, are initially horizontal, each secured on one side to a wall and connected to a mass $m$ on the other. The mass is lowered a height $h$ from its initial position so that the system is in equilibrium.

In terms of the initial length $l$, height $h$, and spring constant $k$, what is the mass $m$?

A

$$\cfrac {2 k h} {g} \cdot \frac {h} {\sqrt{l^{2}+h^{2}}}$$

B

$$\cfrac {2 k h} {g} \cdot (1-\cfrac {h} {\sqrt{l^{2}+h^{2}}})$$

C

$$2k \cdot \cfrac {\sqrt{l^{2}+h^{2}} - l} {g}$$

D

$$2k \cdot \cfrac {\sqrt{l^{2}+h^{2}}} {g}$$

E

$$\cfrac {2 k h} {g} \cdot (1-\cfrac {l} {\sqrt{l^{2}+h^{2}}})$$

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