Chapter 12 Oscillations i. Period(周期)7 Frequency(频率fand Angular Frequency(角频率或圆频率): 周期、频率 = AcosTA(+T)+)/xx-t图 x=Acos(at+o) Acos(ot++aT)O ◆周期.2z 振动往复一次所需时间。 The time required for one complete cycle. Cycle refers to the complete to-and-fro motion from some initial point back to that same point
Chapter 12 Oscillations ii. Period(周期)T, Frequency(频率)f and Angular Frequency (角频率或圆频率) : ➢ 周期、频率 2π 周期： T = x = Acos(t +) cos( ) cos[ ( ) ] A t T A t T = + + = + + x −t 图 A − A x T 2 T t o 振动往复一次所需时间。The time required for one complete cycle. Cycle refers to the complete to-and-fro motion from some initial point back to that same point
Chapter 12 Oscillations ◆频率fT2 单位时间内振动的次数。单位:Hz Where frequency (), or number of oscillations that are completed each second. Its sI unit is the hertz (hz) I hertz=l hz=1 oscillation per second =l s ◆角频率0=27 2m秒内的振动次数。(单位:1/S或rad/S) o Is called angular frequency(角频率) of the motion
Chapter 12 Oscillations 2 1 = = T f = 2 f 频率 单位时间内振动的次数。单位：Hz Where frequency (f ), or number of oscillations that are completed each second. Its SI unit is the hertz (Hz) 1 hertz = 1 Hz = 1 oscillation per second = 1 s-1 Is called angular frequency（角频率） of the motion. 角频率 2秒内的振动次数。（单位：1/S或rad/S)
Chapter 12 Oscillations Q,,ν都表示简谐运动的周期性,反映振动的快慢。 k 11k am 2兀=2兀 T 2Im Vk T and f is also called intrinsic period or frequency(固有周期和固有频率)— ensure b system property They dont depend on the amplitude
Chapter 12 Oscillations m k = k m T 2 2 = = m k T f 2 1 1 = = T and f is also called intrinsic period or frequency (固有周期和固有频率.)⎯⎯ ensure by system property. They don’t depend on the amplitude. ,T, 都表示简谐运动的周期性，反映振动的快慢
Chapter 12 Oscillations i. Phase or Phase angle& Initial~(相位和初相p301 or a certain oscillatory object, A and a are fixed. At any time, its motion state(x& v) will be determined by (at +o. So(at +o is called hase 在x=Acos(at+g)中,x+9称为振动的相位 1)O+q->x,存在一一对应的关系;即其决定 质点在时刻的t的位置。 2)相位在0~2兀内变化,质点无相同的运动状态 相差2n(i整数点运动状态全同.(周期性)
Chapter 12 Oscillations iii. Phase or Phase Angle & Initial ~(相位和初相p301) For a certain oscillatory object, A and are fixed. At any time, its motion state ( x & v) will be determined by (t +). So (t +) is called phase. 在 x = Acos(t +) 中， t + 称为振动的相位。 1） ，存在一一对应的关系;即其决定 质点在时刻的t的位置。 t + → x 2）相位在 0 ~ 2π 内变化，质点无相同的运动状态； 相差2nπ (n为整数 )质点运动状态全同.（周期性）
Chapter 12 Oscillations 3)初相位φ(t=0)描述质点初始时刻的运动状态 (φ取[一兀→>]或[O→>27]) (o is the phase at t=0--initial phase)
Chapter 12 Oscillations (o is the phase at t = 0 —– initial phase) 3）初相位 (t = 0) 描述质点初始时刻的运动状态. ( 取 [−π →π] 或 [0→2π] )