What is the differential equation of motion in if kinetic friction (but no other damping

Chapter 3, Problem 54

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What is the differential equation of motion in if kinetic friction (but no other damping forces) acts on the sliding mass? [Hint: Assume that the magnitude of the force of kinetic friction is A = mg, where mg is the weight of the mass and the constant > 0 is the coefficient of kinetic friction. Then consider two cases: x' > 0 and x' < 0. lnteJpret these cases physically.]

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