find the work done by spring force in stretching from x1 to x2
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Answer:
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where k is spring constant, measured experimentally for a particular spring. The value of k (=-F/x) measures the stiffness of the spring. A high value indicates that we would require to apply greater force to change length of the spring.
This relationship, defining spring force, is also known as “Hooke’s law”, which is valid under two specific conditions :
The mass of spring is negligible (and can be neglected).
There is no dissipative force (like friction) involved with spring.
The attribute “x” is measured from the position of “neutral length” or “relaxed length” - the length of spring corresponding to situation when spring is neither stretched nor compressed. We shall identify this position as origin of coordinate reference.
The negative sign in the expression indicates an important aspect of the nature of spring force that it is always opposite to the direction of the displacement. It means that it is always directed towards the position at neutral length i.e. origin. See the figure to visualize how spring force is always directed towards origin.
Explanation: