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A large spring has a force constant of $1000\ \text{N/m}$ and is initially stretched $2\ \text{meters}$ beyond its equilibrium length.

By how much does the spring's elastic potential energy increase if the spring is stretched from $2\ \text{meters}$ to $3\ \text{meters}$?

A

$500\ \text{J}$

B

$2000\ \text{J}$

C

$2500\ \text{J}$

D

$4500\ \text{J}$

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