An object is attached to a vertical spring and bobs up and down between points a and b. where is the object located when its elastic potential energy is a minimum

The elastic potential energy of a spring is given by

where k is the spring constant and x is the displacement of the spring with respect to its rest position.

Looking at the formula, we can see that E is minimum (zero) when x=0, so when it's at rest position. This means that the elastic potential energy of the system is minimum (zero) when the object is crossing the rest position of the spring.

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