A particle executes simple harmonic motion with a time period of 12 s . The minimum time taken by the particle to travel from a position equal to half of its amplitude to the positive extreme position is

Step-by-step solution

Let the equation of motion of the particle starting from the mean position be x = A ( t) . The time t₁ taken to reach half the amplitude ( x = A 2 ) is given by: A 2 = A ( t₁) t₁ = 6 The time t₂ taken to reach the positive extreme position ( x = A ) is given by: A = A ( t₂) t₂ = 2 The time taken to travel from x = A 2 to x = A is: t = t₂ - t₁ = 2 - 6 = 3 Since = 2 T , we have: t = 3 ( 2 T ) = T 6 Given T = 12 s , the required time is: t = 12 6 = 2 s Answer: 2 s