. A text book of physics, for the use of students of science and engineering . (Fig. 251). It will be noted that the accelera-tion is directed constantly towards O. From (3), a has zero valuewhen sin a=0, when a = 0 or ir; M will then be passing throughO. Maximum values of a occur when sin a= ± 1, when M is atN and again at S ; in these positions <W-±£=±o*R (6) Displacement, velocity and acceleration diagrams for M have beendrawn in Figs. 252 (a), (6), and (c) for values of a from 0 to 2tt. Itis evident that the displacement and acceleration graphs are curvesof sines, and that the
. A text book of physics, for the use of students of science and engineering . (Fig. 251). It will be noted that the accelera-tion is directed constantly towards O. From (3), a has zero valuewhen sin a=0, when a = 0 or ir; M will then be passing throughO. Maximum values of a occur when sin a= ± 1, when M is atN and again at S ; in these positions <W-±£=±o*R (6) Displacement, velocity and acceleration diagrams for M have beendrawn in Figs. 252 (a), (6), and (c) for values of a from 0 to 2tt. Itis evident that the displacement and acceleration graphs are curvesof sines, and that the velocity graph is a curve of cosines. Further,since a is proportional to t, it follows that these diagrams are alsodisplacement, velocity and acceleration graphs on time bases ; thebase line O to 2tt represents the time of one revolution of P (), or the time of one complete vibration of M from N to S andback to N. This time is called the period of the vibration. 222 DYNAMICS CHAP. Let T = the period, thenvT = 2ttR (Fig. 251),2ttR T = v 2-R_2tT wR w Displacement. •(7) .(7) FIG. 252.—Graphs for simple harmonic motion. The frequency of the vibration is the number of vibrations persecond, and is obtained by taking the reciprocal of T : thus Frequency = n=- vibrations per sec. .(8) Example. A point describes simple harmonic vibrations in a line4 cm. long. Its velocity when passing through the centre of the line is12 cm. per second. Find the period. XVI SIMPLE HARMONIC VIBRATIONS 223 The given maximum value of V is also the velocity of P in the circum- ference of the circle (Fig. 251) ; hence T = 2ttR_2 x22x2v 12x7 1-05 seconds. A well-known mechanism in which simple harmonic motion isrealised is shown in Fig. 253. A crank revolves in the dotted circleabout a fixed centre and engages a blockwhich may slide in a slotted bar. Rodsattached to the bar are guided so as to becapable of vertical motion only. The effectof the slot is to cancel the horizontal com-ponents of th
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