Bob and light string
Concentrate the moving mass in a small bob suspended from a string whose mass and extension can be neglected.
Physics / Simple pendulum
FREE TO EXPLOREEXPERIMENT 02 · PHYSICS LABORATORY
Acceleration due to gravity with a simple pendulum
Determine gravitational acceleration from the gradient of a graph of period squared against pendulum length. Explore a virtual apparatus, collect readings and analyse a graph.
CHANGE · OBSERVE · MEASURE
Your virtual workbench.
TIME FOR 20 OSCILLATIONS—
MEASUREMENT STATUS
Ready for a virtual observation.
Use ≤5° and keep amplitude fixed for a measurement series.
Adjust the apparatus, then take a reading.
Timing is generated from the model; a short on-screen trial represents a longer physical interval. Animation is illustrative.
Simulation assumptions and limits
This virtual experiment assumes a point bob, a massless inextensible string, a fixed frictionless pivot, planar small-angle motion and uniform gravity. It neglects damping, finite-bob inertia, support movement and finite-amplitude period changes. Timing displays represent accelerated simulated time rather than wall-clock measurements. Rounded model readings may create small fit residuals; these are not empirical measurement uncertainty. The reference 9.80665 m/s squared is a chosen standard model parameter, not a claim about gravity at your location. The timing model includes the leading finite-amplitude correction T ≈ 2π√(L/g)[1 + θ₀²/16 + 11θ₀⁴/3072], with θ₀ in radians. The simple graph analysis neglects this correction, giving a small systematic bias even at 3°. Angles above 5° remain available for exploration but cannot be recorded.
Know your apparatus.
Rigid support and clamp
Provide a fixed pivot and allow the effective pendulum length to be changed.
Metre rule and angle guide
Measure pivot-to-bob-centre length in metres and set an initial angle no larger than 5 degrees.
Timer and reference marker
Measure elapsed time for 20 complete oscillations using a consistent crossing and direction.
FOLLOW THE METHOD
A reason behind every step.
Determine gravitational acceleration from the gradient of a graph of period squared against pendulum length. Suggested independent settings: 0.35, 0.5, 0.65, 0.8, 1.0 m.
Define the length
Set a pivot-to-bob-centre length and record L in metres. Begin near the middle of the available range.
Why this step matters
Using the string length alone produces a systematic length error.
Set a small release
Displace the bob by no more than 5 degrees. Release it without a push and keep motion in a single vertical plane.
Why this step matters
A small, clean release matches the assumed simple harmonic motion.
Time 20 cycles
Choose one direction of crossing at the centre. Start at crossing zero and finish at crossing 20 in the same direction. Read the elapsed virtual time in seconds.
Why this step matters
A consistent phase and cycle count avoids half-period and off-by-one errors.
Repeat and vary length
Repeat timings if available, then use at least five lengths across the permitted range. Keep the angle small for every run.
Why this step matters
Repeats assess scatter and a spread of lengths constrains the graph gradient.
Process observations
For each length calculate mean elapsed time, T = mean time/20, and T squared. Keep unrounded values for the fit and round only table display values.
Why this step matters
Early rounding can bias the gradient and the final estimate.
Fit and interpret
Fit T squared against L with an intercept. Calculate g = 4pi squared/gradient, state units, inspect the intercept and residuals, and discuss uncertainties before comparing with the model reference.
Why this step matters
A reported result needs both a numerical estimate and an assessment of what the data support.
YOUR NOTEBOOK · 0 OBSERVATIONS
Turn measurements into a result.
Points are your observations. The fit uses SI x and y values before display scaling.
LINEAR FIT · y = mx + b
T² = mL + b; g = 4π²/m
| # | Pendulum length L (m) | Time for 20 oscillations (s) | Length L (m) | Period squared T² (s²) | Remove |
|---|
No readings yet. Take a virtual measurement and record it.
Calculate it yourself.
CHECK YOUR UNDERSTANDING