physics • mechanics

Coupled Oscillators

Explore two coupled masses on springs, normal modes, energy transfer, and beat phenomena. Watch x₁ and x₂ oscillate together in superposed normal modes.

SYSTEM PARAMETERS

Mass m₁ (kg)

1.0 kg

Mass m₂ (kg)

1.0 kg

Spring k₁ (N/m)

2.0 N/m

Spring k₂ (N/m)

2.0 N/m

Spring k₃ (N/m)

2.0 N/m

Initial x₁ (m)

0.8 m

Initial x₂ (m)

0.0 m

Initial v₁ (m/s)

0.0 m/s

Initial v₂ (m/s)

0.0 m/s

Simulation Speed

1.0x

Position x₁(t)

Position x₂(t)

Phase Space: x₂ vs x₁ (Lissajous)

Normal Mode q₊ (In-Phase)

Normal Mode q₋ (Out-of-Phase)

Real-Time Statistics

0.00

x₁ (m)

0.00

x₂ (m)

0.00

v₁ (m/s)

0.00

v₂ (m/s)

0.00

Total E (J)

0.00

ω₊ (rad/s)

0.00

ω₋ (rad/s)

Beat Period (s)