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(D) The mechanical energy $E$ of a harmonic oscillator is proportional to the square of its amplitude $A$,given by $E = \frac{1}{2} k A^2$.For a small

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$3$

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(D) The mechanical energy $E$ of a harmonic oscillator is proportional to the square of its amplitude $A$,given by $E = \frac{1}{2} k A^2$.For a small change in amplitude,the fractional change in energy is given by the differential:$\frac{dE}{E} = \frac{d(A^2)}{A^2} = \frac{2A dA}{A^2} = 2 \frac{dA}{A}$.Given that the amplitude decreases by $1.5 \%$,we have $\frac{dA}{A} = 1.5 \%$.Substituting this value into the expression for fractional change in energy:$\frac{dE}{E} = 2 	imes 1.5 \% = 3 \%$.Thus,the mechanical energy lost in each cycle is $3 \%$.

If the amplitude of a lightly damped oscillator decreases by $1.5 \%$,then the mechanical energy of the oscillator lost in each cycle is: (in $\%$)

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