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Q.

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

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a

μmgk

b

2μmgk

c

μgk

d

kμmg

answer is B.

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Detailed Solution

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