If a freely suspended object is pulled to one side and released, it oscillates about the point of suspension because the

Step 1: Analyze the question A pendulum-like object is pulled aside and released. We are asked why it oscillates about the point of suspension, so we need the condition that produces oscillatory (simple harmonic) motion.

Step 2: The concept An object performs simple harmonic motion (SHM) when its acceleration is:

• directly proportional to its displacement from the equilibrium position, and
• always directed towards the equilibrium position (hence the negative sign).

Mathematically: a = -ω²x

The restoring force (for a pendulum, a component of the weight, mg sinθ) always pulls the object back toward the equilibrium point. For small displacements this force is proportional to the displacement, so the acceleration is too.

Step 3: Check each option

• A. Acceleration is directly proportional to the displacement. Correct. This is the defining condition for SHM (a ∝ -x).
• B. Motion is directed away from the equilibrium point. Wrong. The restoring force is directed towards equilibrium, otherwise the object would never return.
• C. Acceleration is directly proportional to the square of the displacement. Wrong. The relationship is linear (a ∝ x), not a ∝ x².
• D. Velocity is minimum at the equilibrium point. Wrong. Velocity is maximum at equilibrium and zero at the extreme positions.

Step 4: Answer

Exam tip: Remember the SHM keywords: "a ∝ -x". Any option saying acceleration is proportional to displacement (not displacement squared) is usually the SHM answer. Also remember: at equilibrium, velocity is maximum and acceleration is zero; at the extremes, velocity is zero and acceleration is maximum.