Simple Harmonic Motion Displacement Graph

Steps:

• Identify the motion type from the problem: object undergoes simple harmonic motion (SHM).
• Recall the displacement equation: s = A sin(ωt + φ), producing sinusoidal variation with time.
• Examine graph options: look for periodic oscillation starting from equilibrium or amplitude.
• Select the graph matching sine/cosine wave without damping or irregularities.

Why A is correct:

• Graph A shows sinusoidal displacement oscillating between +A and -A, directly following Hooke's law and SHM definition.

Why the others are wrong:

• B: Linear increase indicates constant velocity, not oscillatory SHM.
• C: Parabolic shape suggests accelerated motion like free fall, not periodic.
• D: Constant displacement violates SHM's restoring force requirement.

Final answer: A