Physics · Class 11

Drive an oscillator near resonance

A periodic force drives a damped oscillator most strongly near its resonance. Damping broadens and lowers the response peak. The settled motion lags behind the driving force; free oscillations decay with an exponential envelope.

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Drive an oscillator near resonance

இயக்க அதிர்வெண் இயல்பான அதிர்வெண்ணுக்கு அருகில் இருந்தால் வீச்சு அதிகம். தணிப்பு அதிகரித்தால் ஒத்திசைவு உச்சம் குறையும்.

Key notes, relationships and model limits

Key relationship

A=F₀/√((k−mω²)²+(bω)²); phase=atan2(bω,k−mω²); free envelope∝e^(−bt/(2m)).

Remember

Common trap

The forced-response peak is not always exactly at the undamped natural frequency.

Model limits

Linear damped oscillator under sinusoidal forcing. Response curve is the settled steady state, not the initial transient. Damping is positive; resonance frequency can differ from the undamped natural frequency.

What you will learn

Read a resonance curve and explain damping and phase lag.

Try the experiment

Try both scenarios, change one control, and predict the result before checking the graph and readouts.

Think of it this way

Change one input while keeping the others fixed, as you would in a controlled experiment.

Worked example

For m=1 kg, k=16 N/m, b=1 kg/s and F₀=1 N, ω₀=4 rad/s and A at ω₀ is 1/4=0.25 m with a π/2 phase lag.

Why this matters

The model connects drive an oscillator near resonance with an observable reading. Check the equation and assumptions before applying it.

Before you start

SI units · algebra · graph reading

Check your understanding

At ω=√(k/m), what is the steady-state amplitude?

F₀/k
F₀/(bω)
F₀/(mω²)

Read the explanation

The spring and inertia terms cancel at that frequency, leaving denominator bω.

Course connection: Class XI Chapter 13. Consult the roadmap for CBSE, NEET, JEE Main and Advanced scope.