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I was taught in school that the magnitude of the kinetic frictional force does not depend on the speed.

Hence, the equation of motion of the harmonic oscillator in the presence of friction with the floor would be

$$m\ddot{x}=-kx-f\frac{\dot{x}}{|\dot{x}|}$$

However, the damped harmonic oscillator is modeled with friction proportional to velocity.

$$m\ddot{x}=-kx-c\dot{x}$$

This may consider air resistance to be linearly dependent on velocity, but I don't see why kinetic friction would disappear. Is it assumed that there is no friction with the floor?

Pekaron
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  • Related post by OP: https://physics.stackexchange.com/q/705894/2451 – Qmechanic Apr 30 '22 at 10:18
  • 'In many vibrating systems the frictional force Ff can be modeled as being proportional to the velocity v of the object: Ff = −cv, where c is called the viscous damping coefficient.' does this not help? – Dirac Delta Yeah Apr 30 '22 at 17:39
  • And your force for friction, assuming its given as $f=\mu_fN$ where N is the normal force of the mass, is not correct at the force of friction always acts to oppose the direction of motion i.e. it should be negative – Dirac Delta Yeah Apr 30 '22 at 17:41
  • @DiracDeltaYeah Does that “many vibrating systems” include cases where there is kinetic friction with the floor and where Stokes' law does not hold? – Pekaron Apr 30 '22 at 19:11

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