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A special spring is constructed in which the restoring force is in the opposite direction and is proportional to the cube of the displacement i.e. F=-k (x^3) spring is stretched a distance of A and then released what is the potential energy of the spring at the instant it is released? the spring is on a horizontal friction less surface

What is the definition of work? Force times distance, right? So the work done in stretching the spring should be equal to the potential energy of the spring when it is stretched. Now in this case the force varies as the spring is stretched (as x^3) so you cannot just do a straight product, you have to integrate the force from x = 0 to x = A. If you know calculus, you should see the answer now. If you do not, I cannot think of any way to do this problem without it...

Arthur Smith

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