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Total energy that is lost in the spring=1/2 mv

^{2}+mgx

When the spring is compressed for x m, it has 1/2 (F) (x) J of energy, right?

So to find the average F exerted by spring, should I combine the two equations together to find f?

However, my teacher said that the first equation should be linked to Fx as work is done by the ball. Thats another way of looking at it though, but the answer is different obviously. How do you explain it? I know it is my misunderstanding, can anyone help me see the light?

Thanks.