A pendulum swings back and forth. At what point in its swing is its kinetic energy greatest?

A pendulum demonstrates the conservation of mechanical energy. Energy converts between gravitational potential energy (PE = mgh) and kinetic energy (KE = ½mv²). At the highest points (the extremes of the swing): the pendulum is momentarily stopped, velocity = 0, so KE = 0. All energy is potential. At the lowest point: pendulum is at its fastest, maximum KE. All energy has converted to kinetic (height is at minimum). At intermediate points: some kinetic, some potential. Total mechanical energy (KE + PE) is constant in an ideal frictionless pendulum. In reality, air resistance and pivot friction gradually convert mechanical energy to thermal energy, causing the swing amplitude to decrease over time (damping) until the pendulum stops. Pendulum period: T = 2π√(L/g), where L is length and g is gravity. Period depends ONLY on length and gravity — NOT on mass or amplitude (for small angles). Longer pendulum = slower swing. Used in: grandfather clocks (controlled timing), Foucault pendulum (demonstrates Earth's rotation), seismographs (modified versions detect earthquakes). Similar energy transformations: (1) ROLLER COASTER — height to speed; gravity does the work going down, speed climbs back to nearly equal height (some energy lost to friction); (2) BOUNCING BALL — gravitational PE → kinetic → elastic PE (compression) → kinetic → gravitational; energy lost each bounce as heat/sound; (3) SPRING — elastic PE ↔ kinetic in oscillation; (4) PROJECTILE — KE ↔ gravitational PE at peak height. Conservation principle: in absence of non-conservative forces (friction, air resistance), total mechanical energy is conserved.