Dynamics of linear elastic SDOF oscillators

This chapter addresses the dynamic response of single-degree-of-freedom (SDOF) oscillators in the linear elastic domain, with emphasis on ground-induced excitation. It develops the equation of motion, discusses solution approaches and presents the representation of response using pseudo-acceleration, velocity, and displacement spectra. The equations governing structural dynamics are easily established based on Newton's first two laws of motion. The momentum of a body is a vector quantity given by the product of mass and velocity. Resonance is the tendency of a system to oscillate with large peak amplitude under forced vibration at particular frequencies, known as the system's resonant frequencies. Earthquake ground motion is conveniently defined by acceleration records obtained in three orthogonal directions from a seismograph. The time derivative of the relative displacement time history is the relative velocity time history; its time derivative is the relative acceleration time history.