Key relationship
T≈2π√(L/g)(1+θ₀²/16); gsmall=4π²L/T².
Physics · Practical apparatus
Pendulum length and stopwatch
Time many cycles to reduce the effect of stopwatch resolution. Adjust bob mass to confirm the ideal period is independent of mass; use the length to the centre of the bob.
Open the interactive experiment →Pendulum length and stopwatch
பல அலைவுகளை அளந்து காலத்தைப் பெறவும். இலட்சிய ஊசல் காலம் நிறையைச் சாராது; நீளத்தின் வர்க்கமூலத்தைச் சாரும்.
Key notes, relationships and model limits
Practical tip
Time many cycles to reduce the effect of stopwatch resolution. Adjust bob mass to confirm the ideal period is independent of mass; use the length to the centre of the bob.
Common trap
Measure length from the support to the bob’s centre. Time several complete oscillations and divide by their number.
Model limits
small-amplitude pendulum with first amplitude correction. Stopwatch rounds total time; inferred g deliberately uses the common small-angle formula and uncorrected stopwatch offset.
What you will learn
Adjust pendulum length and stopwatch apparatus, observe its reading and derive the indicated physical quantity.
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
L=1 m and g=9.81 m/s² give T≈2.006 s in the zero-amplitude limit.
Why this matters
The model connects pendulum length and stopwatch with an observable reading. Check the equation and assumptions before applying it.
Before you start
SI units · algebra · graph reading
Check your understanding
Quadrupling pendulum length changes its small-angle period by?
- A factor of four.
- A factor of two.
- A factor of one half.
Read the explanation
A factor of two.
Course connection: Virtual apparatus preparation. Check exact board/exam membership in the syllabus sources. Physical practical work remains necessary.