In a mass-spring system undergoing simple harmonic motion, which equation correctly gives acceleration a in terms of displacement x?

• A. a = -kx/m
• B. a = kx/m
• C. a = -(m/k) x
• D. a = -x/m

Answer: (A)

When a mass on a spring is displaced, the spring pulls back toward the equilibrium position with a force proportional to the displacement: F = -kx. Applying Newton's second law, F = ma, gives ma = -kx, so the acceleration is a = -kx/m. The negative sign is essential: it means the acceleration is directed opposite to the displacement, pulling the mass back toward equilibrium and producing the characteristic back-and-forth motion of simple harmonic motion. The magnitude of acceleration grows with how far you pull the mass, and the motion’s frequency is set by sqrt(k/m). The other forms either drop the restoring direction or mix in factors that don’t have the correct units, so they don’t describe the actual acceleration in SHM.