A particle executes simple harmonic motion between x = -A and x = +A about its mean position x = 0 . If the time taken by the particle to travel from x = 0 to a position x = x₁ is equal to the time taken to travel from x = x₁ to x = A , then the value of x₁ is:

Step-by-step solution

Let the time period of the simple harmonic motion be T . The total time taken by the particle to travel from the mean position x = 0 to the extreme position x = A is T 4 . It is given that the time taken to travel from x = 0 to x = x₁ is equal to the time taken to travel from x = x₁ to x = A . Therefore, the time taken to reach x₁ from the mean position is exactly half of the time taken to reach the extreme position. Time taken to reach x₁ , t = 1 2 T 4 = T 8 . The equation for the position of the particle starting