Time intervals and repeated pendulum oscillations
Choose a timer for the interval and time several complete cycles to find a mean period.
Exam scope and assessment notes
Mapped to the named 0973 section using teaching from the corresponding single-science course. A 0973-specific review of every Core and Supplement objective is still in progress. Written practice is self-checked; it does not demonstrate supervised laboratory competence or award an official Cambridge grade. This qualification reports two grades on the 9–1 scale; confirm the entry route for your zone and exam series.
Before you begin
- Read seconds and minutes.
- Divide a duration by a cycle count.
Work on paper. Try each question before revealing help, and explain why your method works.
Quick readiness check
What is one complete pendulum oscillation?
What you will learn
- Measure a time interval using a clock or digital timer.
- Calculate a pendulum period from multiple complete oscillations.
Define the start and stop events
A clock can measure a long interval by subtracting start and finish times. A digital stopwatch can measure shorter intervals from elapsed time, but its display resolution is not the same as the person's start/stop reaction time. An automated timer with sensors can avoid manual triggering if suitable for the event.
Specify the events being timed, such as passage of a bob through a fixed central reference point in the same direction. Return to the same position with the same direction of motion defines one complete pendulum oscillation. A centre crossing in the opposite direction marks only half an oscillation.
Time many cycles and repeat
For a securely mounted small-amplitude pendulum in supervised practical work, time a known number of complete oscillations, then divide the elapsed time by that number. Twenty oscillations taking 32.0 s give a mean period of 1.60 s. This makes the total interval longer without changing the definition of a period.
Repeat the total-time measurement with the same length and similar small amplitude, compare results and average consistent trials. Timing twenty cycles reduces the relative effect of start/stop reaction compared with timing one; it does not remove miscounting, a changing setup or every source of uncertainty. Paper exercises interpret supplied data and do not replace supervised practical experience.
Sources for this lesson
Pause and explain
Twenty complete oscillations take 32.0 s. What is the period?
Worked example
Twenty complete oscillations take 31.8 s, 32.2 s and 32.0 s in three trials. Find the mean period.
Show the worked solution
- Mean total = (31.8 + 32.2 + 32.0)/3 = 32.0 s.
- Each trial contains twenty complete oscillations.
- Period = 32.0/20 = 1.60 s.
Answer 1.60 s.
Try a topic test
Choose Easy, Normal or Difficult. Save your answers and open worked review after finishing.
Test this topic →From guided practice to a new situation
Write your answer and reasoning first. Use a hint only if you are stuck. The model solution is for self-checking; your written work is not automatically marked.
Twenty cycles take 32.0 s. Find the mean period.
Give me a hint
The measured interval contains twenty periods.
Compare my reasoning
- Identify the cycle count twenty.
- Calculate 32.0/20.
- State the period 1.60 s.
1.60 s.
Look for these in your work
- Use complete cycles.
- Give seconds.
Fifteen oscillations take 27.3 s. Calculate the mean period.
Give me a hint
Divide the duration by fifteen rather than timing a half-swing.
Compare my reasoning
- Use total time 27.3 s.
- 27.3/15 = 1.82.
- Record period 1.82 s.
1.82 s.
Look for these in your work
- Use the supplied count.
- Keep time per cycle.
A student times each successive centre crossing, even when the direction reverses. Explain the period error and a better reference rule.
Give me a hint
A return needs the same position and direction.
Compare my reasoning
- Successive opposite-direction centre crossings are half a cycle apart.
- Calling that interval a period gives half the true period.
- Start and stop at centre crossings in the same direction and count complete cycles.
The reported period is halved; use same-direction crossings.
Look for these in your work
- Recognise a half-cycle.
- Define repeatable endpoints.
Common mistakes
- A period is a complete cycle, not one half-swing.
- The stopwatch decimal places do not establish reaction-time accuracy.
- Divide by the oscillation count, not the number of trials twice.
What can you explain now?
Ten complete oscillations take 18.0 s. What is the mean period?
Compare with the explanation
1.80 s.
A complete period is the total duration divided by the ten cycles.
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Make it stick
Describe a twenty-cycle timing method and explain why it helps without making the measurement exact.
If you needed the solution, close it and solve the problem again from a blank page. A correct answer is stronger when you can explain the reason for each step.