2 The needle of a sewing machine is made to oscillate vertically through a total distance of 22 mm. as shown in Fig. 3.1. 22mm needle at its maximum height Fig. 3.1 The oscillations are simple harmonic with a frequency of 4.5 Hz. The cloth that is being sewn is positioned ELI] mm below the point of the needle when the needle is at its maximum height. {a} State wl'iat is meant by simple harmonic moo'on. [2] {hi The displacement y of the point of the needle may he represented by the equation y = a costar. [it Suggest the position of the point of the needle at time 1': iii. [1] {ii} Determine the values of 1. a. a = .......................................... mm [1] 2. m a: = ..................................... rad s'1 [2] (c) Calculate, for the point of the needle, (1) its maximum speed, speed = . . ....... ms [2] (li) its speed as it moves downwards through the cloth. speed = ......... ms"[3]