A particle is executing simple harmonic motion. If the minimum time taken by the particle to move from extreme position to half of the amplitude is t₁ , and the minimum time taken by the particle to move from mean position to half of the amplitude is t₂ , then

Step-by-step solution

For the particle to move from extreme position to half of the amplitude aligned & x = A t ₁ & A 2 = A t ₁ & t ₁= 3 aligned For the particle to move from mean position to half of the amplitude aligned & x=A t₂ ; A 2 =A t₂ & t₂= 6 & t₁ t₂ = 3 6 t₁=2 t₂ aligned