Physic Labs

Oscillations and waves

Damped and driven oscillations; resonance

Study the response curve of a damped, driven oscillator: measure the steady-state amplitude A/A0A/A_0 versus frequency ratio f/f0f/f_0 and verify the resonant frequency fr≈f01−b2/2f_r \approx f_0\sqrt{1 - b^2/2}.

High school

Equipment

  • Canvas plotting the driven-oscillation amplitude curve versus drive frequency, rotated by dragging or arrow keys
  • Sliders «Tần số riêng f₀», «Tần số kích thích f» and «Lực cản tương đối b»
  • Readout line showing the ratio «f/riêng», «biên độ ổn định tương đối A/A₀» and «tần số cộng hưởng xấp xỉ»
  • «Tạm dừng» / «Chạy tiếp» button to freeze the curve

Procedure

  1. Read the resonance peak at the initial settings

    Keep «Tần số riêng f₀» = 100 Hz and «Lực cản tương đối b» at a small value. Inspect the curve: the amplitude peak sits near f₀, and the red dot marks the selected frequency. Read «tần số cộng hưởng xấp xỉ» on the readout line and compare with fr≈f01−b2/2f_r \approx f_0\sqrt{1 - b^2/2}.

  2. Sweep the drive frequency across resonance

    Drag «Tần số kích thích f» from low to high through f₀. Record «biên độ ổn định tương đối A/A₀» at a few f values — especially at the peak. For f << f₀, A/A₀ ≈ 1; for f >> f₀, A/A₀ → 0; the largest amplitude occurs near frf_r. Check that the «f/riêng» ratio is then close to 1.

  3. Change damping and watch the peak shape

    Increase «Lực cản tương đối b» and repeat the sweep: the resonance peak becomes lower and broader, and «tần số cộng hưởng xấp xỉ» shifts below f₀ according to fr≈f01−b2/2f_r \approx f_0\sqrt{1 - b^2/2}. Press «Tạm dừng» to record the two curves before comparing.

  4. Predict and conclude about resonance

    Set «Tần số riêng f₀» to a new value, predict the peak position and «tần số cộng hưởng xấp xỉ» before looking at the readout. Conclude: the driven amplitude is largest when the drive frequency is near the natural frequency, and the weaker the damping the sharper the resonance peak.

Simulation

Experiment history

Resonance was observed early through pendulums and strings: in Dialogue Concerning Two New Sciences (1638) Galileo Galilei described how a string can sound by itself when excited at its own frequency. Newton and the mechanicians of the seventeenth and eighteenth centuries laid the basis for analysing oscillating systems under damping and periodic forcing. In the nineteenth century Hermann von Helmholtz used spherical resonators to analyse the frequency content of sound — a direct application of the response curve. In engineering, the 1940 collapse of the Tacoma Narrows Bridge is often taught as the classic lesson on large resonant response of a structure under periodic wind excitation, although the true mechanism was aeroelastic flutter.

Related physicists

Galileo GalileiIsaac Newton

Related library topics

Damped and driven oscillations; resonance