Unit 7 · Oscillations

Simple harmonic motion ● (core concept) — Periodic motion produced when the restoring force on an object is proportional to its displacement from the equilibrium position, as with an ideal spring.

Restoring force ● (core concept) — A force directed opposite the displacement and back toward the equilibrium position, where the net force on the system is zero.

Pendulum as SHM ○ — A pendulum swinging through small angles approximates simple harmonic motion, because its restoring torque is nearly proportional to its angular displacement.

Period of a mass-spring oscillator ● (core concept) — T = 2π·√(m/k): heavier masses and weaker springs oscillate more slowly.

Period of a simple pendulum ● (core concept) — For small angles, T = 2π·√(L/g): longer pendulums swing more slowly, independent of the bob's mass.

Period and frequency ● (core concept) — Period and frequency are inverses of each other: T = 1/f. This relation applies to simple harmonic motion just as it does to uniform circular motion.

SHM position function ● (core concept) — The displacement of a simple harmonic oscillator follows x = A·cos(2π·f·t) (or a sine form), where A is the amplitude.

Amplitude and period ● (core concept) — Changing the amplitude of a simple harmonic oscillator does not change its period.

Velocity and acceleration in SHM ● (core concept) — Speed is greatest at the equilibrium position and zero at the turning points; acceleration is greatest at the turning points and zero at equilibrium. These maxima and zeros can be read from SHM graphs.

Energy of SHM ● (core concept) — A simple harmonic oscillator's total energy E = K + U is conserved: kinetic energy peaks when potential energy is lowest and vice versa. The amplitude sets the total energy — for a spring oscillator, E = ½·k·A².