A particle performs SHM of time period T. Find the time taken by the particle to go directly (i) from its mean position to half the amplitude and (ii) from half the amplitude position to its positive extreme position.

A particle performs SHM of time period T. Find the time taken by the p

1.	A particle performs SHM of time period T. Find the time taken by the particle to go directly (i) from its mean position to half the amplitude and (ii) from half the amplitude position to its positive extreme position.
Answer» Solution :When a particle is INITIALLY in the mean position, `X= ASIN omegat` i) When the particle travels from mean position to half its amplitude, DISPLACEMENT, `x = A//2`. `(A)/(2)= Asinomegat` `sinomegat= (1)/(2) implies omegat= (PI)/(6) implies (2pi)/(T)t=(pi)/(6) implies t= (T)/(12)` ii) The time taken to go from half the amplitude position to its positive extreme position = [Time taken to go from mean to positive extreme position]-[Time taken to go from mean to half amplitude position] `= (T)/(4)- (T)/(12)= (T)/(6)`