Free Fall and Harmonic Oscillators
This chapter provides some common differential equations that appear in physics. It deals with the simplest types of equations and standard techniques for solving them. As an object falls faster and faster, the drag force becomes greater. So, this resistive force is a function of the velocity. The next physical problem of interest is that of simple harmonic motion. Such motion comes up in many places in physics and provides a generic first approximation to models of oscillatory motion. Simple harmonic motion is an ideal situation. A special type of forcing is periodic forcing. Realistic oscillations will dampen and eventually stop if left unattended. For example, mechanical clocks are driven by compound or torsional pendula, and electric oscillators are often designed with the need to continue for long periods of time.