# Work Done by Spring force and variable force

Work done by a variable force:-
Let us considered a force which acts always in One Direction but whose magnitude may keep on varying. We can choose the direction of the force as the x-axis. Further, let us assume that the magnitude of the force is also a function of x is known to us. Now, we are interested in finding the work done by this force in moving a body from $$X_{i} to X_{f}$$.

Work done for small displacement $$d{x}$$ is

$$dW=F\cdot dx$$

Now total work done can be obtained by integration of the above formula from the lower limit to an upper limit.