Two particles are executing SHM in a straight line. Amplitude A and time period T of both the particles are equal. At time t = 0, one particle is at displacement x_(1) = +A and the other at x_(2) = (-A)/(2)and they are approaching towards each other. After what time they cross each other?

Two particles are executing SHM in a straight line. Amplitude A and ti

1.	Two particles are executing SHM in a straight line. Amplitude A and time period T of both the particles are equal. At time t = 0, one particle is at displacement x_(1) = +A and the other at x_(2) = (-A)/(2)and they are approaching towards each other. After what time they cross each other?
Answer» Solution : Equations can be written as : `x_(1)= A cosomegat` and `x_(2)= A sin(omegat-pi//6)`Here `OMEGA= (2pi)/(T)` Equating `x_(1)= x_(2) "" Sin(omegat- (pi)/(6))= cos omegat` `Sinomegatcos((pi)/(6))-sin((pi)/(6))cosomegat= cosomegat` `SINOMEGAT(sqrt(3))/(2)-(1)/(2)cosomegat= cosomegat` `tan omegat= sqrt(3), omega= (2pi)/(T), t= (pi)/(3),` we get `t= T//6`