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