Two simple harmonic oscillators with amplitudes in the ratio 1:2 are having the same total energy, the ratio of their frequencies is

if amplitude A1=A    then  A2=2A total energy of both oscillators is same total energy=12mw2A2      12mw12A12=12mw22A22 ⇒  12mw12A2=12mw2222A2   ⇒ w21w22=4 take square root ⇒ w1w2=2 ⇒2πf12πf2=2    ⇒f1f2=2 \