Given a harmonic oscillator driven by a sweeping frequency:
$$\frac{\mathrm{d}^2x}{\mathrm{d}t^2} + 2\zeta\omega_0\frac{\mathrm{d}x}{\mathrm{d}t} + \omega_0^2 x = \frac{1}{m} F_0 \sin\left(\omega(t) t\right), $$ with $\omega(t)=x_{Trianlge}(t)+\omega_t$. $x_{Trianlge}(t)$ being the triangle wave. $\omega_t$ doesn't need to be resonance frequency $\omega_0$, but we know that $\omega_0$ lies in the range of the sweep.
Can this be solved analytically?