4.7. Particular Motions#

In this section, we will study certain particular motions that are interesting and useful to analyze for educational, historical, and practical reasons.

  • Uniform rectilinear motion

  • Uniformly accelerated motion

  • Uniform circular motion

  • Oscillatory and damped oscillatory motions:

    • Free oscillations:

      • Mass-spring(-damper) system

      • Pendulum

    • Forced oscillations:

      • A first step towards structural analysis and beyond (“every physical system is a system of many harmonic oscillators”)

      • Concepts of frequency response and resonance. todo video and/or script on frequency response of structures and seismic structures, mass-damper,…

  • Gravitation: Starting from Newton’s universal law of gravitation, we study the motion of celestial bodies in two-body systems, discovering that their trajectories describe conic sections (circle, ellipse, parabola, hyperbola), and demonstrating Kepler’s laws.

  • Rotation of a body around a fixed point, Poinsot’s motions