(Solved): A 2.0kg simple harmonic oscillator has a natural (angular) frequency of 4 s ...

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A $2.0\mathrm{kg}$ simple harmonic oscillator has a natural (angular) frequency of 4 ${\mathrm{s}}^{?1}$. It is immersed in a linear medium with a linear drag coefficient of 4.0 $\mathrm{N}?\mathrm{s}/\mathrm{m}$. It is subject to an external (co)sinusoidal driving force of maximum magnitude $6.0\mathrm{N}$. Consider the large time behaviour of the system. a) [3] At what (angular) frequency do we need to drive the oscillator at so that the amplitude of the oscillations at large times is maximal? (Show your work, and express as an exact value.) b) [1] If we drive the oscillator at the frequency you found in part a), what is the exact (irrational) amplitude of the oscillations at large times (in m)? Simplify your answer to the form $\frac{a}{\sqrt{b}}$.