Which of the following best explains why a pendulum released from a small initial angle can be modeled as executing simple harmonic motion?
(a) At small angles, the gravitational force on the bob is essentially constant in direction and magnitude, so its tangential acceleration is uniform.
(b) At small angles, the mass of the bob cancels from the period equation T=2πL/g, so the motion depends only on string length and therefore must be simple harmonic.
(c) At small angles, sinθ≈θ, so the tangential component of the gravitational force (and thus the restoring torque) is directly proportional to the angular displacement, satisfying the condition for simple harmonic motion.
(d) At small angles, the bob’s path is nearly a circle of fixed radius, so its required centripetal acceleration is almost constant, producing oscillations with a fixed period.