U_g&=U_{sp} && \text{start with by setting the gravitational potential energy equal to the spring potential energy}\\mgh&=\frac{1}{2}k\Delta x^2 && \text{substitute the equations for gravitational and spring potential energy}\\\Delta x&=\sqrt{\frac{2mgh}{k}} && \text{solve for } \Delta x\\\Delta x&=\sqrt{\frac{2*2\;\text{kg} * 9.8\;\text{m/s}^2 * 5\;\text{m}}{3000\;\text{N/m}}} && \text{plug in the known values}\\\Delta x&=.26\;\text{m}\\
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