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

Options

A. `(mu mg)/(k)`
B. `(2mu mg)/(k)`
C. `(mu g)/(k)`
D. `(k)/(mumg)`

Answer

B

Explanation

(b) From -a to b decrease in elastic potential energy
= work done against friction.
`:. " "(1)/(2)ka^(2)-(1)/(2)kb^(2)=mumg(a+b)`
or `" " (a-b)=(2mumg)/(k)`
`:. "Decrease in amplitude"=(2mumg)/(k)`