The x–t graph of a particle performing simple harmonic motion is shown in the original figure. The particle has x = +1 m at t = 2 s, x = 0 at t = 4 s, x = -1 m at t = 6 s, and x = 0 at t = 8 s. The acceleration at t = 2 s is:
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Question

The x–t graph of a particle performing simple harmonic motion is shown in the original figure. The particle has x = +1 m at t = 2 s, x = 0 at t = 4 s, x = -1 m at t = 6 s, and x = 0 at t = 8 s. The acceleration at t = 2 s is:

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G1 Physics · Accepted Answer

Step 1: From the graph, maximum +1 m at t = 2 s and minimum −1 m at t = 6 s are separated by T/2 = 4 s. Step 2: Hence T = 8 s and ω = 2π/T = π/4 rad s⁻¹. Step 3: At t = 2 s the displacement is x = +1 m. Step 4: SHM acceleration is a = −ω²x = −(π/4)² × 1 = −π²/16 m s⁻². Final answer: (B) −π²/16 m s⁻².

The x–t graph of a particle performing simple harmonic motion is shown in the original figure. The particle has x = +1 m at t = 2 s, x = 0 at t = 4 s, x = −1 m at t = 6 s, and x = 0 at t = 8 s. The acceleration at t = 2 s is: