The first and second derivatives are: dzdt=−iωe−iωtd2zdt2=−ω2e−iωt Substituting these into the differentia...The first and second derivatives are: dzdt=−iωe−iωtd2zdt2=−ω2e−iωt Substituting these into the differential equation gives: [−ω2−2iγω+ω20]e−iωt=0. This equation holds for all t if and only if the complex second-order polynomial on the left-hand side is zero: −ω2−2iγω+ω20=0. The solutions for ω can be …
