A Heavier Pendulum Bob Does Not Swing Any Slower
Learn how time was measured before clocks, what a pendulum's time period means, why only its length matters, and how to convert confidently between time units.
How did people measure time before clocks existed?
By watching things that repeat reliably. The Sun rising and setting marked days, the changing Moon marked months, and the seasons marked years. From those natural repetitions came devices that measured shorter stretches of time.
This page covers everything in the CBSE Class 7 Science chapter on the measurement of time: the early time-measuring devices, the simple pendulum and its time period, what the period does and does not depend on, and converting between units of time.
This page covers everything in the CBSE Class 7 Science chapter on the measurement of time: the early time-measuring devices, the simple pendulum and its time period, what the period does and does not depend on, and converting between units of time.
What were the sundial, water clock and sand clock?
Each early device used something that changed at a steady rate.
A sundial uses the shadow of a rod falling on a marked surface. As the Sun moves across the sky the shadow sweeps around, and its position indicates the time. Its obvious limitation is that it is useless at night or under cloud.
A water clock measures time by water dripping steadily from one vessel into another, the level showing how much time has passed.
A sand clock, or hourglass, lets sand run through a narrow neck between two glass bulbs. When the upper bulb empties, a fixed interval has passed, and it is turned over to start again.
A candle clock is a candle marked at intervals along its length; as it burns down past each mark, that much time has gone.
For example, a kitchen egg-timer is a sand clock still in everyday use.
What all four share is a repeating or steady process. That is the requirement for measuring time — and it is exactly what makes a swinging pendulum so useful.
A sundial uses the shadow of a rod falling on a marked surface. As the Sun moves across the sky the shadow sweeps around, and its position indicates the time. Its obvious limitation is that it is useless at night or under cloud.
A water clock measures time by water dripping steadily from one vessel into another, the level showing how much time has passed.
A sand clock, or hourglass, lets sand run through a narrow neck between two glass bulbs. When the upper bulb empties, a fixed interval has passed, and it is turned over to start again.
A candle clock is a candle marked at intervals along its length; as it burns down past each mark, that much time has gone.
For example, a kitchen egg-timer is a sand clock still in everyday use.
What all four share is a repeating or steady process. That is the requirement for measuring time — and it is exactly what makes a swinging pendulum so useful.
What are the parts of a simple pendulum?
A simple pendulum is a small heavy bob tied to one end of a light thread, with the other end fixed to a rigid support such as a clamp stand or a hook.
Its mean position is where the bob hangs at rest, straight down. Pull the bob slightly to one side and release it, and it swings back and forth through that mean position.
One complete oscillation is one full to-and-fro swing: the bob goes from one extreme position, across to the other extreme, and back again to where it started.
The time period is the time taken for one complete oscillation.
The support must be rigid, because if it moves or sags the swing is disturbed and the readings become unreliable.
The counting mistake to avoid: a single journey from one side to the other is only half an oscillation. Counting those as full swings doubles your answer.
Its mean position is where the bob hangs at rest, straight down. Pull the bob slightly to one side and release it, and it swings back and forth through that mean position.
One complete oscillation is one full to-and-fro swing: the bob goes from one extreme position, across to the other extreme, and back again to where it started.
The time period is the time taken for one complete oscillation.
The support must be rigid, because if it moves or sags the swing is disturbed and the readings become unreliable.
The counting mistake to avoid: a single journey from one side to the other is only half an oscillation. Counting those as full swings doubles your answer.
Formula
How do you measure the time period, and what does it depend on?
One swing is too quick to time accurately, so measure many and divide:
Worked example. A pendulum takes 40 seconds to complete 20 oscillations, so
Now the experiment that gives this article its title. Repeat the measurement while changing one thing at a time:
- Change the mass of the bob, keeping the thread the same length: the time period stays the same.
- Change the length of the thread, keeping the bob the same: the time period changes — a longer thread gives a longer period.
So the time period depends on the length of the thread, and not on the mass of the bob.
That is exactly why timing 20 oscillations beats timing one: your reaction-time error is spread across twenty swings instead of landing entirely on a single reading.
Worked example. A pendulum takes 40 seconds to complete 20 oscillations, so
Now the experiment that gives this article its title. Repeat the measurement while changing one thing at a time:
- Change the mass of the bob, keeping the thread the same length: the time period stays the same.
- Change the length of the thread, keeping the bob the same: the time period changes — a longer thread gives a longer period.
So the time period depends on the length of the thread, and not on the mass of the bob.
That is exactly why timing 20 oscillations beats timing one: your reaction-time error is spread across twenty swings instead of landing entirely on a single reading.
Formula
How do you convert between seconds, minutes and hours?
The second (s) is the SI unit of time. The conversions are:
Worked example. Convert 2.5 hours into seconds:
Worked example the other way. Convert 450 seconds into minutes:
A combined one. A pendulum with a time period of 2 s completes how many oscillations in 5 minutes? Five minutes is s, so
Always convert to a single unit before dividing. Mixing minutes and seconds inside one calculation is where numerical answers in this chapter go wrong.
Worked example. Convert 2.5 hours into seconds:
Worked example the other way. Convert 450 seconds into minutes:
A combined one. A pendulum with a time period of 2 s completes how many oscillations in 5 minutes? Five minutes is s, so
Always convert to a single unit before dividing. Mixing minutes and seconds inside one calculation is where numerical answers in this chapter go wrong.
Exam tip
The mistake most students make counting oscillations
Students count each time the bob passes them, which counts half-swings and halves the time period.
Fix a clear rule before starting: choose one extreme position, and count one oscillation each time the bob returns to that same extreme having gone all the way across and back. Do not count from the mean position, where the bob passes twice per oscillation.
And time a large number of oscillations — twenty is standard — then divide. Starting the stopwatch as you release the bob adds a reaction-time error, and spreading that error over twenty swings makes it twenty times smaller in the final answer.
Fix a clear rule before starting: choose one extreme position, and count one oscillation each time the bob returns to that same extreme having gone all the way across and back. Do not count from the mean position, where the bob passes twice per oscillation.
And time a large number of oscillations — twenty is standard — then divide. Starting the stopwatch as you release the bob adds a reaction-time error, and spreading that error over twenty swings makes it twenty times smaller in the final answer.
Did you know
Why does a pendulum make such a good timekeeper?
Because its time period stays essentially the same swing after swing, and does not change as the swing gets smaller. A pendulum slowing down still keeps time.
That steadiness is the whole reason pendulum clocks work. The swing provides a repeating interval of fixed length, and the clock's gears simply count those intervals.
That steadiness is the whole reason pendulum clocks work. The swing provides a repeating interval of fixed length, and the clock's gears simply count those intervals.
Key takeaways
Measuring time: quick revision
- Early devices used steady or repeating processes: the sundial's shadow, the water clock's drip, the sand clock's flow and the candle clock's burning.
- A simple pendulum is a bob on a light thread from a rigid support; one complete oscillation is a full to-and-fro swing, and its time is the time period.
- Time period = total time ÷ number of oscillations, so timing twenty swings reduces reaction-time error.
- The time period depends on the length of the thread and not on the mass of the bob.
- The second is the SI unit of time; 1 minute = 60 s and 1 hour = 3600 s, and you must convert to one unit before calculating.
You will remember all of this far better after answering five questions on it than after reading it twice.
- A simple pendulum is a bob on a light thread from a rigid support; one complete oscillation is a full to-and-fro swing, and its time is the time period.
- Time period = total time ÷ number of oscillations, so timing twenty swings reduces reaction-time error.
- The time period depends on the length of the thread and not on the mass of the bob.
- The second is the SI unit of time; 1 minute = 60 s and 1 hour = 3600 s, and you must convert to one unit before calculating.
You will remember all of this far better after answering five questions on it than after reading it twice.