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The stochastic dynamics of the damped harmonic oscillator in a heat bath issimulated with an algorithm that is exact for time steps of arbitrary size.Exact analytical results are given for correlation functions and power spectrain the form they acquire when computed from experimental time-lapse recordings.Three applications are discussed: (i) Effects of finite sampling-rate and-time, described exactly here, are similar for other stochastic dynamicalsystems-e.g. motile micro-organisms and their time-lapse recorded trajectories.(ii) The same statistics is satisfied by any experimental system to the extentit is interpreted as a damped harmonic oscillator at finite temperature-such asan AFM cantilever. (iii) Three other models of fundamental interest arelimiting cases of the damped harmonic oscillator at finite temperature; itconsequently bridges their differences and describes effects of finite samplingrate and sampling time for these models as well. Finally, we give a briefdiscussion of nondimensionalization.

Harmonic Oscillator in Heat Bath: Exact simulation of time-lapse-recorded data, exact analytical benchmark statistics