Harmonic oscillations
Motion that repeats at equal time intervals is periodic; periodic motion about an equilibrium position is oscillatory. Oscillations of a body displaced from equilibrium under internal forces are free (natural) oscillations. The distance of the body from equilibrium is the displacement x, and the largest displacement is the amplitude A. If the displacement changes with time by a sine (or cosine) law, the oscillation is harmonic: x = A sin(ω₀t + φ₀), where ω₀ is the angular frequency, (ω₀t + φ₀) is the phase and φ₀ the initial phase. The period is T = t/N (time of one full oscillation), the frequency is ν = N/t = 1/T (unit 1 Hz = 1 s⁻¹) and the angular frequency is ω = 2π/T = 2πν (rad/s). The velocity is υ = Aω cos(ωt + φ₀) and the acceleration a = –ω²x; the velocity amplitude is Aω and the acceleration amplitude Aω². Oscillations need a restoring force, inertia of the body and little friction.
In class with the teacher: with a watch or phone stopwatch measure the time of 20 oscillations of a weight on a string and compute the period and frequency. Use a small light weight and a long string, away from other people.