simple harmonic motion

Meaning: Oscillation about an equilibrium position where the net force is a restoring force, proportional to the displacement and directed back toward equilibrium. Position varies sinusoidally with time. Speed is greatest at equilibrium, where acceleration is zero. At the turning points (x = ±A, where A is the amplitude) speed is zero and acceleration is greatest. Total energy, ½kA², is constant in the ideal case.

Equation: F = −kx and T = 2π√(m/k). F is the restoring force (N), k the spring constant (N/m), x the displacement from equilibrium (m), T the period (s), m the mass (kg). For a pendulum at small angles, T = 2π√(L/g), with L the length (m) and g the gravitational acceleration (m/s²).

On the MCAT: Passages give a mass on a spring or a pendulum and ask how period or frequency changes with mass, k or length, or where speed, acceleration or kinetic energy is at a maximum. Figures are often sinusoidal position-versus-time graphs.

Common confusion: A larger amplitude does not lengthen the period, because a larger displacement brings a proportionally larger force. A pendulum's period also does not depend on its mass, and the pendulum formula holds only for small angles.