When the magnitude and direction of a force vary in three dimensions, it can be expressed as a function of the position vector (r), or in terms of the coordinates (x, y, z). The work done by such a force in an infinitesimal displacement ds is
W = .d
If x be the displacement of the free end of the spring from its equilibrium position then, the magnitude of spring force is given by
Fx = -kx
The negative sign signifies that the force always opposes the extension (x > 0) or the compression (x < 0) of the spring. In other words, the force tends to restore the system to its equilibrium position
The work done by the spring force for a displacement from xi to xf is given by
or Ws =
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