Other types of damping

An object of mass $m$ is attached to an ideal spring ($k$) and driven by an external force $F_{\rm ext}(t) = F_0 \cos(\omega t)$. The drag force exerted on the object is given by $F_{\rm drag} = -cm\frac{d^3x}{dt^3}$.

(a)

Find the (real) amplitude $A$ of oscillations.

Hint: As in class, assume that the oscillations are harmonic and use the complex representation.

(b)

For $\omega_o = 100$ sec$^{-1}$ and $c=\frac{1}{2\omega_o}$, sketch $A/\frac{F_o}{m}$ versus $\omega$.