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Physics · Class 11

Tune a small-angle pendulum

Oscillations

At small angles the pendulum has a restoring acceleration proportional to angular displacement. A longer string increases period, while greater gravity decreases it. The ideal small-angle period is independent of bob mass.

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Tune a small-angle pendulum

சிறிய கோண ஊசலின் காலம் 2π√(L/g). நீளம் அதிகரித்தால் காலம் அதிகரிக்கும்; நிறை அதை மாற்றாது.

Key notes, relationships and model limits

Key relationship

T=2π√(L/g); θ(t)=θ₀cos(√(g/L)t).

Remember

At small angles the pendulum has a restoring acceleration proportional to angular displacement. A longer string increases period, while greater gravity decreases it. The ideal small-angle period is independent of bob mass.

Common trap

Large-amplitude pendulum motion does not have exactly this amplitude-independent period.

Model limits

Point bob on a massless inextensible string; no air resistance, small angle ≤15°. Period formula omits finite-amplitude correction and bob mass does not enter.

What you will learn

Relate pendulum geometry and gravity to small-angle timing.

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 L=1 m and g=9.8 m/s², T=2.007 s. At lunar gravity 1.6 m/s² the same pendulum has T=4.967 s.

Why this matters

The model connects tune a small-angle pendulum with an observable reading. Check the equation and assumptions before applying it.

Before you start

SI units · algebra · graph reading

Check your understanding

How does period change when length quadruples?

Read the explanation

T is proportional to √L.

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