Simple’HarmonicMotion’ Ryerson Department （简单HarmonicMotionu201C瑞尔森）.pdfVIP

Simple Harmonic Motion Many physical systems exhibit a predictable oscillatory behaviour that can be described mathematically by a sinusoidal wave. A few examples include the motion of a pendulum, the oscillation of a spring-mass system, the oscillation of charge carriers in an inductor-capacitor electrical circuit, or the variation in pressure at the mouth of a bottle when airflow causes an audible resonance. The mathematical physics describing these systems is fundamentally identical, and because of the oscillatory nature of their behavior they are said to exhibit simple harmonic motion (SHM). The mathematical similarity between such systems stems from the nature of the forces present. In each case, a displacement from equilibrium generates a restoring force proportional to the displacement. For example, in the case of the spring-mass system we’ll investigate, Hooke’s Law describes the force caused by a displacement from equilibrium according to the formula: F = -kx. These systems exhibiting SHM all possess a physical parameter (analogous to x in Hooke’s Law above) which behaves as a sinusoidal function of time, such that: x(t) = A sin(2πf t+φ) where: x(t) is the parameter that exhibits SHM (i.e. position, charge, pressure) t is time A is the amplitude of the parameter f is the frequency of the behavior (related to period, T, by: T=1/f ) φ is called a phase constant” which describes the initial condition of the parameter. In this laboratory we focus on studying the position of a mass in a spring-mass system as a function of time. Figure 1. Example of spring- mass configuration and