Experiments you can run yourself.
The simple pendulum: why the period does not depend on mass or amplitude, only on length. Interactive simulation, the formula T = 2π√(L/g), determining the gravitational acceleration g.
Damping dissipates the energy of oscillations, so the amplitude decreases over time: x(t)=A·e^(−βt)·cos(ω′t). Stronger damping → faster decay. Critical damping gives the fastest return without oscillations.
The amplitude of forced vibrations is largest when the driving frequency equals the natural frequency f₀. The maximum of the resonance curve is always at f₀.
Potential and kinetic energy flow back and forth, while their sum stays constant.
Two close tones give a pulsation at frequency |f₁−f₂|.