Driven – Consider a driven damped oscillator given by the differential equation d²x dx .. m dt2 + my di + mwăx =qEoeiwt

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Driven Consider A Driven Damped Oscillator Given By The Differential Equation D X Dx M Dt2 My Di Mwax Qeoeiwt 1 (159.77 KiB) Viewed 42 times

Driven – Consider a driven damped oscillator given by the differential equation d²x dx .. m dt2 + my di + mwăx =qEoeiwt (a) Explain the physical significance of each term. (b) We look for a steady state solution and hence use the trial solution of the form X = Xoeilwt-a) where Eo, Xo, w and a are all real quantities. Substitute into the differential equation and show that qE. Xo = m[(wą – w2)? +7222] 2 (Hint: find an expression for x, and since it is real, its complex conju- gate will be equal to itself. Then take the product to eliminate a and get the result.) and tan a = 2 wa - w2 (Hint: go back to the expression for Xo and since it is real set its imaginary part to zero. It will help to write eia = cos a + i sin a. ) 7w