12 . The displacement , in centimetres , of a particle from an origin , O , at time t t seconds , is given by s( t) � 8e sin3t
, 0 �t � � .
( a ) Find the maximum distance of the particle from O .
( b ) ( i ) Find the time when the particle first goes back to O .
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( ii ) Find s� () t .
( iii ) Hence , write down the acceleration of the particle at the instant it first goes back to O .
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