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(a) Suppose we represent the motion of a simple harmonic oscillator ("SHO") using complex notation: x(t) = Re [ã(t)] x(t) = a(t) + ib(t) (6) (7) -iwt xe (8) Where here a and b are just the real and imaginary part of ã. Note that we are using the Griffiths convention for the time dependance (-iwt) instead of the French convention (+iwt). For all parts below you may assume this is a SHO with mass m and spring constant k so that W = √k/m. Find the real velocity of the resonator, v(t) 𐐀x = Ot a and b. (There should be no à да ь მხ Express your answer in terms of tx, or in your final answer.) = - Ət'
(b) Find the kinetic and potential energy (K and U) of the resonator in terms of a and b. (There should be no à da i ab x, or x in your final answer.) Ət ' It' (c) Find the total energy of the resonator, E = K +U, in terms of ã. (There should да в = ot, a, b, or x in your final answer.) be no à = მხ Ət'