The displacement time graph of a particle executing SHM is given in figure: (sketch is schematic and not to scale) Which of the following statements is/are true for this motion? (A) The force is zero at t = 3 T 4 (B) The magnitude of acceleration is maximum at t = T (C) The speed is maximum at t = T 4 (D) The P . E . is equal to K . E . of the oscillation at t = T 2

Step-by-step solution

From graph equation of SHM. X = A cos ω t (A) at 3 T 4 particle at mean position ∴ a = 0 F = 0 (B) at T particle again at extreme position so acceleration is maximum (C) at t = T 4 , particle is at mean position so velocity maximum. ∴    a = 0 (D) K E = P E 1 2 k A 2 - x 2 = 1 2 k x 2 A 2 = 2 x 2 x = + A 2 A 2 = A cos ω t t = T 8 ∴   A ,   B and C are correct.