Novel analytical solutions are presented for single-degree-of-freedom (SDOF) oscillators founded on footings and piles on compliant ground. First, exact formulas are derived for the fundamental viscoelastic natural period and effective damping of these structures. It is shown that certain approximations proposed in the literature may be inaccurate for highly-damped systems. Second, the influence of foundation mass on natural period and damping is investigated. Third, the effect of coupled swaying-rocking oscillations at the pile head is addressed by translating the reference system to the location down the pile, where the resultant soil reaction is applied.
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