Planning a pendulum investigation
Model pendulum timing, plot period squared against length and compare timing allowances. This simulation supports rather than replaces practical work.
Learning goals
- Use SI quantities, units, prefixes and dimensional analysis.
Current setup: a pendulum of length 0.60 metres, release angle 10 degrees and declared count N = 1. The ideal point-mass model uses a light, inextensible suspension and fixed g = 9.81 metres per second squared. It has no damping, air resistance or string mass; bob mass does not change its period. Press the stopwatch to start a new timing. No completed timing yet. The 0.2 second elapsed-time allowance is illustrative, not measured from your clicks.
- Stopwatch
- 0.00 s
- Period from last completed timing, T = t / N
- — s
- Illustrative fractional timing allowance: current setup
- 13 %
- Timing model
- Δt = 0.2 s per elapsed timing: assumed, not measured from clicks.
- Last completed timing
- No completed timing yet
- Recorded-data check
- Record at least 4 distinct lengths for the gradient estimate.
- g from the recorded free-intercept fit
- — m s−2
Try this
0 of 4 doneSet N to 20 or more, complete a timing trial and compare the illustrative fractional allowance. (not done yet)
For a fixed elapsed-time allowance Δt, ΔT = Δt/N. The lab cannot verify your cycle count or measure your reaction-time error; use equivalent crossings in the same direction.
Record at least 5 distinct lengths covering 0.3 m to 1.0 m. (not done yet)
Well-spaced lengths across a wide range can make the trend and gradient easier to estimate. Check scatter, controls and the model as well.
Use at least 4 distinct lengths at one fixed release angle of 15° or less to estimate g within 3% of 9.81 m s⁻². (not done yet)
The displayed fit has a free intercept. For a controlled small-angle series, its slope gives g = 4π²/m. Inspect the intercept and residuals; a plausible g alone does not validate the model.
Time the same length at 15° or less and again at 40° or more. (not done yet)
The ideal nonlinear model predicts a longer period at larger angles. Compare the recorded periods and timing allowances; merely making two timings does not establish a measured difference. Keep this comparison separate from the small-angle length series.
You’ve tried every task.
Your readings
| # | l / m | N | t / s | T2 / s2 | release angle / ° | Remove |
|---|---|---|---|---|---|---|
| No readings yet. Set up a measurement, then record it. | ||||||