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## Homework Statement

Reading chapter 4 of Morin's "Introduction to classical mechanics" I came across to the explanation of the damped harmonic motion.

The mass m is subject to a drag force proportional to its velocity, ##F_f = -bv ##.

He says that the total force of the mass is ##F= -b \dot{x} -kx## and considering that ##F= m\ddot{x} ## we get this differential equation $$ \ddot{x} +\frac{b}{m} \dot{x} + \frac{k}{m} x=0$$

But the total force should be ##F= -b \dot{x} +kx##, shouldn't it? These two forces have opposite direction!