Question

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?

Answer 1

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.