Two particles P and Q start from origin at the same time and execute simple harmonic motion along x-axis with same amplitude but with periods 3 sec and 6 sec respectively. The ratio of the speeds of P and Q when they meet for the first time after start is

(2)xP=A  sin 2π3t  and xa=A sin 2π6t =Asin π3t.VP=dxPdt=  2π3A .  cos 2π3t  and  VQ=dxQdt=  π3A .  cos π3tWhen  xP=xQ,   A  sin 2π3t  =A sin π3t⇒     sin π3t  2cos π3−1 =0when    sin π3t=0    ⇒   t=0when  2cos π3−1=0   ⇒   cos π3t=12  =cos π3 ⇒  t=1  S∴  VPVQ=2πA3 .    cos π3.1 πA3     cos π3 = 2.  121/2=2.