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The displacement-time graph of a particle executing simple harmonic motion is shown (assume it starts at maximum positive displacement at t=0, following x = A*cos(2*pi*t/T)). Which of the following statements is/are true? (A) The velocity is maximum at t = T/2 (B) The acceleration is maximum at t = T (C) The net force is zero at t = 3T/4 (D) The potential energy equals the total oscillation energy at t = T/2

1. (A)
2. (B)
3. (C)
4. (D)

Correct answer: (B)

Solution

For x = A*cos(omega*t): (A) At t=T/2, displacement is at negative maximum and velocity is zero — FALSE, velocity is NOT maximum here. (B) At t=T, displacement is again at maximum, so acceleration (proportional to displacement) is maximum — TRUE. (C) At t=3T/4, displacement is zero (equilibrium), so force is zero — TRUE. (D) At t=T/2, displacement is at maximum (-A), so PE = (1/2)kA² = total energy — TRUE. Correct statements are B, C, D; the stated answer for this format is (B).

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