Driving forces create steady response—and resonance.

Driving adds energy continuously. The key questions are: how much energy per cycle, and how it depends on frequency and phase.

• What “driving” means physically
• Periodic forcing intuition
• Energy added vs energy lost
• Transient vs steady-state distinction

After transients fade, the oscillator responds at the driving frequency, not necessarily at its natural frequency.

• Why transients disappear with damping
• Response frequency equals driving frequency
• Amplitude depends on frequency
• Phase shift emerges naturally

Resonance occurs when the driving frequency aligns with the system’s natural tendency to oscillate, producing large amplitude response (limited by damping).

• Why resonance increases amplitude
• Damping limits the peak
• Sharp vs broad resonance
• Recognizing resonance graphs

The phase shift tells you whether the oscillator moves in step with the driver or lags behind. Phase changes most rapidly near resonance.

• In-phase vs out-of-phase meaning
• Low-frequency vs high-frequency limits
• Phase behavior near resonance
• Why phase matters for power transfer

Resonance appears in bridges, buildings, musical instruments, and electronics. The physics is the same; the safety implications are not.

• Structural resonance (conceptual)
• Musical resonance and sound amplification
• Vibration control and tuning
• Everyday “resonant response” intuition

Practice reading resonance curves, describing phase behavior, and connecting damping to response.

• Identify resonance frequency from graphs
• Concept checks: damping vs peak width
• Phase-lag interpretation questions
• Energy transfer reasoning prompts
• Exam-style driven-oscillator sets