We use the harmonic-oscillator model to analyze the motion of the sites (ground motion), seimograph recordings, and structures built on the Earth’s surface under the action of the seismic motion. The seismic motion consists of singular waves (spherical-shell P and S primary seismic waves) and discontinuous (step-wise) seismic main shocks. It is shown that these singularities and discontinuities are present in the ground motion, seismographs’ recordings and the motion of the built structures. In addition, the motion of the oscillator exhibits oscillations with its own eigenfrequency, which represent the response of the oscillator to external perturbations. We estimate the peak values of the displacement, the velocity and the acceleration of the ground motion, both for the seismic waves and the main shock, which may be used as input parameters for seismic hazard studies. We discuss the parameters entering these formulae, like the dimension of the earthquake focus, the width of the primary waves and the eigenfrequencies of the site. The width of the seismic waves on the Earth’s surface, which includes the energy loss, can be identified from the Fourier spectrum of the seismic waves. Similarly, the eigenfrequencies of the site can be identified from the spectrum of the site response. The paper provides a methodology for estimating the input parameters used in hazard studies.