A $$mass-spring$$ system oscillates such that the mass moves on a rough surface having coefficient offriction μ. It is compressed by a distance a from its normal length and on being released, it moves to adistance b from its equilibrium position. The decrease in amplitude for one $$half-cycle$$ $$(-a$$ to $$b)$$ is

Question

A $$mass-spring$$ system oscillates such that the mass  moves on a rough surface having coefficient offriction μ. It is compressed by a distance a from its normal length and on being released, it moves to adistance b from its equilibrium position. The decrease in amplitude for one $$half-cycle$$ $$(-a$$ to $$b)$$ is

Infinity Learn · Accepted Answer

From $$-$$ a to b, decrease in elastic potential $$energy=$$ work done against friction.∴  $$12ka2-12kb2=$$μ$$mg(a+b)$$ or $$(a-b)=2$$μmgk∴  Decrease in amplitude  $$=2$$μmgk

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