The amplitude of a lightly damped oscillator decreases by 3.0% during each cycle. what percentage of the mechanical energy of the oscillator is lost in each cycle?

E = ½KA^2 is the mechanical energy of any oscillator. It is the sum of elastic potential energy and kinetic energy. When amplitude A decreases by 3%, then

(E2-E1) / E1 = {½K (A2^2/A1^2) } / ½K (A1^2)

= { (A2^2 - A1^2) / (A1^2) }

= 97^2 - 100^2/100^2

= 5.91% of the mechanical energy is lost each cycle.