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Homework Statement:

The equation is FCoswt = mx'' + myx' +mw_0^2x
 Find the steady state solution for the displacement x and the velocity x'
 Sketch the amplitude and phase of x and x' as a function of w
 Determine the resonant frequency for both the displacement and the velocity
 Defining deltaw as the full width at half maximum of the resonance peak, calculate deltaw/w_0 to leading order in y/w_0
 For a lightly damped driven oscillator near resonance, calculate the energy stored and the power supplied to the system. Confirm that Q = w_0/y.
Homework Equations:
 Steady state solution is the particular solution
I found the steady state solution as
F_0(mw_0^2  w^2m)Coswt/(mwy)^2 + (mw_0^2 w^2m)^2
+ F_0mwySinwt/(mwy)^2 + (mw_0^2 w^2m)^2
But I'm not sure how to sketch the amplitude and phase? Do I need any extra equations?
F_0(mw_0^2  w^2m)Coswt/(mwy)^2 + (mw_0^2 w^2m)^2
+ F_0mwySinwt/(mwy)^2 + (mw_0^2 w^2m)^2
But I'm not sure how to sketch the amplitude and phase? Do I need any extra equations?