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The question is stated as the following:

The correct answer was acquired by using the equation F = mg = -kx, where k is the spring constant and x is the displacement from equillibrium. Using this equation, k is solved as 1,246.6 N/m.

However, in my first attempt at solving, I tried a different method by calculating the amount of work done on the spring and setting that equal to the equation for the elastic potential energy of a spring, U = .5kx

Therefore, .998 = .5kx

What is the reason for this? Why would using this second method not give the correct result for k? Any help/explanation would be greatly appreciated.

When a 3.60 kg object is placed on top of a vertical spring, the spring compresses a distance of 2.83 cm. What is the force constant of the spring?

When a 3.60 kg object is placed on top of a vertical spring, the spring compresses a distance of 2.83 cm. What is the force constant of the spring?

The correct answer was acquired by using the equation F = mg = -kx, where k is the spring constant and x is the displacement from equillibrium. Using this equation, k is solved as 1,246.6 N/m.

However, in my first attempt at solving, I tried a different method by calculating the amount of work done on the spring and setting that equal to the equation for the elastic potential energy of a spring, U = .5kx

^{2}. Calculating the work F*(y_{f}- y_{i}), W = mg*(.0283) = .998 J.Therefore, .998 = .5kx

^{2}. But solving with this method gives k = 2,493.2 N/m, which is not only different from the first result but is exactly double the amount.What is the reason for this? Why would using this second method not give the correct result for k? Any help/explanation would be greatly appreciated.