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.





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