🎛️ Coupled Oscillators Lab

Simulate multi-degree-of-freedom coupled mechanical oscillators. Observe symmetric ($\omega_1$) vs anti-symmetric ($\omega_2$) normal modes and cyclic mechanical energy sloshing ($T_{beat}$).

Oscillator Mass ($m$) kg

Anchor Spring ($k$) N/m

Coupling Spring ($k_c$) N/m

Initial Excitation

Wall —[k]— Mass 1 —[kc]— Mass 2 —[k]— Wall

Mass 1 Energy: 50% Energy Transfer Slosh ($E_1 \leftrightarrow E_2$) Mass 2 Energy: 50%

Symmetric Mode ($\omega_1$)

7.07 rad/s

$\sqrt{k/m}$ (1.13 Hz)

Anti-Symmetric ($\omega_2$)

8.12 rad/s

$\sqrt{(k+2k_c)/m}$ (1.29 Hz)

Beat Period ($T_{beat}$)

5.98 s

Full energy exchange time

Coupling Ratio ($k_c / k$)

0.160

Weak coupling regime