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Another example of conservative force is elastic spring
force.According to Hooke's law the extension of a spring is in direct
proportion with the force applied to it
F   kx, (5.24)

Where
x is the displacement of the spring's end from its equilibrium position
(a distance, in SI units: meters);

F is the restoring force exerted by the spring on that end (in SI units: N
2
or kg·m/s ); and
2
k is a constant called the spring constant (in SI units: N/m or kg/s ).
The negative sign indicates that the force exerted by the spring is in

direct opposition to the direction of displacement. It is called as elastic
spring force or "restoring force", as it tends to restore the system to
equilibrium

Elementary work done by elastic spring force is equal to

dA  Fdx   kxdx. (5.25)

The total work we can calculate as definite integral
x kx 2
A    kxdx   (5.26)

0 2
Consider a spring force acting on a particle, as shown
below(fig. 5.8). The spring is attached to a wall at point O, where it can
pivot. At position A of the particle, the spring is stretched or compressed
by an amount x from its equilibrium ( nonstretched) position. At
1
position B of the particle, the spring is stretched or compressed by an
amount x from its equilibrium position. The arbitrary path travelled by
2
the particle from A to B is represented by the blue curve.

Figure 5.8

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