Consider a frictionless harmonic oscillator (with m = 1) driven by an external force f(t) = A sin(6t) - S0 that d²x/dt² = Asin(ωt). Show that the particular solution for ω ≠ωo is p(t) = sin(ωt - δ), where δ = arctan(ω/6). 14. Suppose that the oscillator in the previous problem is initially in its quiescent state (x(0) = 0, dx/dt(0) = 0) and then the driving force f(t) = A sin(ωt) is imposed. Show that the resulting complete solution is x(t) = (An sin(ωt) + Bn sin(ωot))cos(ωt), where ωo = √(ω² - 36) and An = A/(ω² - ωo²) and Bn = -Aωo/(ω² - ωo²).