A body of mass M is executing simple harmonic motion with an amplitude of 8.0 cm and a maximum acceleration of 100 cm/s². When the displacement of this body from the equilibrium position is 6.0 cm, the magnitude of the acceleration is approximately A) 8.7 cm/s² B) 66 cm/s² C) 35 cm/s² D) 17 cm/s² E) 1.3 m/s²

Question

Quizplus · Accepted Answer

The acceleration in simple harmonic motion is given by a = -ω²x, where ω is the angular frequency and x is the displacement. The maximum acceleration a_max = ω²A, where A is the amplitude. Given a_max = 100 cm/s² and A = 8 cm, we find ω² = 100/8 = 12.5 s⁻². For x = 6 cm, the acceleration a = 12.5 * 6 = 75 cm/s². The magnitude is approximately 66 cm/s².

A Body of Mass M Is Executing Simple Harmonic Motion