Which of the following equation of motion represents simple harmonic motion?

Question

G1 Physics · Accepted Answer

Step 1: For a stable SHM, acceleration is opposite and proportional to displacement from an equilibrium position. Step 2: Option (B) has acceleration a(x) = −k(x + a), where the equilibrium position is x₀ = −a. Step 3: Let ξ = x + a. Then d²ξ/dt² = −kξ, the standard SHM equation for k > 0. Step 4: Option (A) is nonlinear due to x², while (C) and (D) have positive restoring coefficient and unstable equilibrium. Final answer: (B) Acceleration = −k(x + a).