- #1
physconomics
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- 0
- 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.
- Relevant 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?