-
this would become an integral of F, from x1 to x2.
-
And if F really is a function of x
-
and not of also velocity,
-
the laws of calculus tell you,
-
you may write this integral as the difference of two numbers.
-
Then, you rearrange the expression to get K1 + U1;
-
U1 is shorthand for U of x1;
-
is K2 + U2.
-
And that means the energy E1 to begin with, the energy at the end.
-
If there is a frictional force,
-
then in this integral you break it up into two parts:
-
the part, say, due to a spring and the part due to friction.