Forced Oscillation Calculator
Analyze driven harmonic oscillators. Calculate steady-state response, phase lag, resonance, and power absorption.
System Parameters
Natural frequency: 10.0000 rad/s | Resonance: 9.8995 rad/s
Steady-State Amplitude
0.253837 m
Frequency ratio: ω/ω₀ = 0.8000
Resonance Parameters:
Resonance Frequency
9.8995 rad/s
Amplitude at Resonance
0.505076 m
Steady-State Solution:
x(t) = A cos(ωt - φ)
What is Forced Oscillation?
Forced oscillation occurs when an external periodic force is applied to an oscillating system. After initial transients die out, the system reaches a steady state where it oscillates at the driving frequency (not its natural frequency). The amplitude depends on how close the driving frequency is to the natural frequency, reaching maximum at resonance. The response lags behind the driving force by a phase angle that depends on damping and frequency.
Key Concepts
Resonance
Maximum amplitude occurs when driving frequency matches resonance frequency
Phase Lag
Response lags behind driving force; exactly 90° at resonance
Quality Factor
Higher Q means sharper resonance peak and less damping
Power Absorption
Maximum power is absorbed at resonance frequency