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Some more definitions, , Wednesday, January 26,2022 1:18AM, , Displacement, at time t¢, , ZL Phase ‘, , x(t) = X» cos(@t +), , =, , Amplitude Time, Angular Phase, frequency constant, , or phase, angle, , e PHASE OF THE MOTION, The argument of the sine/cosine function is called the phase of the motion. As it varies with time, the value, of the sine/cosine function varies., , ¢ PHASE CONSTANT OR PHASE ANGLE, , It is used to describe the motion regardless of where the particle is in its oscillation when we happen to set, the clock time to Os.

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A positive value of phase angle shifts the curve in the negative direction of the x axis; a negative value of, phase angle shifts the curve in the positive direction., , The amplitudes are different, The amplitudes are the, , but the frequency and same, but the frequencies, , period are the same. and periods are different., x ee, , x T 7, , , , , , , , , , , , , , , , , , 4 t 2 2 < 58 i + é, in S m, kN 7 TA AAA, 2 0 t g 0 t, : tL QQ | OX, Aa —Xin Aa —Xm, oa i T’, , (a) (0), , Figure 15-5 In all three cases, the blue curve is obtained This negative value, , from Eq. 15-3 with ¢ = 0. (a) The red curve differs from re shifts the rocco, , the blue curve only in that the red-curve amplitude 1’, is . curve rightward., , greater (the red-curve extremes of displacement are high- 5, , er and lower). (b) The red curve differs from the blue 5, , curve only in that the red-curve period is 7’ = 7/2 (the red =, , curve is compressed horizontally). (c) The red curve dif- = g=0, , fers from the blue curve only in that for the red curve Thi ;, , & = —7/4 rad rather than zero (the negative value of & win gives 2, , shifts the red curve to the right). () regular cosine curve., , e Angular frequency, , The SI unit of angular frequency is the radian per second, , O= dn ) Tz Tine penod, , T