= Spring-base displacement response with a grounded damper
{title2=$R(\omega)=k/(k-m\omega^2+ib\omega)$}
A spring's support displacement supplies force $kx_1$, while a damper attached to a fixed wall supplies $-b\dot x$. Measuring from static equilibrium gives $m\ddot x+b\dot x+kx=kx_1$. The sinusoidal displacement transfer function is the displayed ratio, with low-frequency limit1 and high-frequency limit $-k/(m\omega^2)$. Moving both the spring and damper supports would introduce a different numerator. A forced particular response must be supplemented by a transient unless initial conditions already select steady motion.
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