A student investigates the relationship between the length L L\,L and the time period T T\,T of a simple pendulum to determine the acceleration due to gravity, ggg. They use the standard model T=2πLg\displaystyle T = 2\pi\sqrt{\frac{L}{g}}T=2πgL. During the experiment, they measure T T\,T for a range of release angles θ \theta\,θ up to 45∘ 45^\circ\,45∘ and observe a systematic deviation in their calculated value of g g\,g as the angle θ \theta\,θ increases.
Which statement represents the correct scientific interpretation of this result?
The standard model must be rejected entirely as incorrect, because a valid scientific model must hold true under all experimental conditions.
The deviation is due to systematic experimental error, and the student should improve their measurement technique to make the results fit the model at all angles.
The model is a simplified representation based on the approximation sinθ≈θ\sin\theta \approx \thetasinθ≈θ, meaning it is only valid for small amplitudes and must be refined for larger angles.
The student should average the calculated values of ggg across all angles to cancel out the variations and validate the small-angle model.