A particle executes simple harmonic motion with an amplitude A and a maximum speed v₀ . The minimum time required for the particle to move from a point where its speed is v₀ 2 to a point where its speed is zero is:

Step-by-step solution

The maximum speed of the particle in SHM is given by v₀ = A , where is the angular frequency. The speed of the particle at any position x is given by: v = A^2 - x^2 When the speed is v₀ 2 , we have: A 2 = A^2 - x^2 Squaring both sides: A^2 4 = A^2 - x^2 x^2 = 3A^2 4 x = 3 A 2 The speed of the particle is zero at the extreme position, x = A . The time taken to travel from the mean position x = 0 to x = 3 A 2 can be found using x = A ( t) : 3 A 2 = A ( t₁) t₁ = 3 t₁ = 3 The time taken to travel from the mean position