A particle executing SHM while moving from one extremity is found at distance x1, x2 and x3 from the centre at the end of three successive seconds. The time period of oscillation is (where θ = cos-1(x1+x32x2))

Displacement-time equation of the particle will beX = A cos ωtGiven that x1 = A cos ω and x2 = A cos 2ωNow, x1+x32x2 = A(cos θ+ cos 3ω)2Acos 2ω                        = 2 A cos 2ω cos ω2A cos 2ω                           = cos ωω = cos-1(x1+x32x2) = 2πTor T = 2πθ where θ = cos-1(x1+x32x2)