大学物理chap12-oscillation.ppt

* Chapter 12 Oscillations Concepts of Simple Harmonic Motion Expression Methods of SHM Energy in SHM Pendulums Superposition of Oscillations Oscillations (振动) —–– motions that repeat themselves. ——— Fundamental physical phenomena and basic constituent of wave motion. We limit our considerations largely to 1D systems ——motion can be described by a single variable. In each system, the displacement varies sinusoidally with time. The sine and cosine functions are called harmonic functions, and this type of motion is referred to as simple harmonic motion (SHM) (简谐振动）. 12-1 Oscillations (P297) x t o T 2T 合振动 分振动1 分振动2 12-2 Concepts of Simple Harmonic Motion (SHM) The simple harmonic motion is the most simple and basic vibration. Every complicated vibration can be considered as composing of several SHM (简谐振动是一种最简单最基本的振动,一切复杂的振动都可以看作是若干简谐振动的合成的结果). Any motion that repeats itself at regular intervals is called periodic motion or harmonic motion. As the “snapshots” (快照）of a SHS, a particle moving repeatedly back and forth about the origin of an x axis. Periodic motion is regular, and repeats with a characteristic (特征）time. 1. Features of SHM Object: block-spring system; Origin: equilibrium position The small-amplitude vibration (小幅振动) for the spring, From Hooke’s Law: Applying N-II law: 2. Motion function of SHM (P299) The solution of this derivation equation is: —— Oscillation Equation Feature of Oscillatory Motion: Dynamics: Kinematics: Motion function is sine or cosine form. Let 3. Basic quantities of SHM (P301) For the motion function of SHM: Where xm (A), ?, and ? are constants. They are basic characteristic quantities of a SHM (描述简谐振动的特征量) . m ii. Period(周期)T, Frequency(频率)f and Angular Frequency (角频率或圆频率)? : i. Amplitude (振幅) xm or A (A 0): —– Initial condition of oscillation ) ( arctan o x v w f - = o w p 2 = T p w 2 1 = = T f f p w 2 = Where frequency (f ), or number of oscillations that are completed each second. Its SI unit is the hertz (Hz) 1 her