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Physics Topics can be challenging to grasp, but the rewards for understanding them are immense.

## Modern Basis of Measuring Time: Periodic Motion

A motion which repeats itself at regular intervals of time is called periodic motion. The principle of periodic motion is used for the measurement of time. Clocks and watches are the most common time-measuring devices used by us.

Clocks and watches which are used for measuring time are based on the principle of periodic motion. One of the most common devices which shows periodic motion is the ‘simple pendulum’.

The pendulum clock used for measuring time is based on the periodic motion of a pendulum. So, before we describe a pendulum clock, we should know the working of a simple pendulum. This is described below.

### Simple Pendulum

A simple pendulum consists of a small metal ball (called bob) suspended by a long thread from a rigid support, such that the bob is free to swing back and forth. A simple pendulum is shown in Figure (a), in which the bob A is suspended by thread from a rigid support.

The motion of pendulum was first studied by Galileo. Galileo discovered the important principle of pendulum according to which : A pendulum completes every swing (or every oscillation) in exactly the same time, provided its length is kept constant. In other words, the time-period of oscillation of a given pendulum is constant.

A simple pendulum can be made by tying about one metre long thread to a small metal ball (called bob) and suspending it from a rigid support as shown in Figure (a), so that the bob is free to swing. When the pendulum is at rest, then its bob is at the mean position A [see Figure (b)].

If the bob of this pendulum is pulled to one side and then released, it will begin to oscillate to-and-fro (back and forth) like a swing [see Figure (b)]. For example, in Figure (b), initially the bob is at the mean position A. Now, suppose the bob is pulled a little to the right side to position B and then released.

It will be seen to come back and move on to position C, at an equal distance on the other side of the mean position A, and then go on repeating this back and forth motion between the two extreme positions B and C. And we say that the simple pendulum is oscillating (or vibrating).

The to-and-fro motion of a simple pendulum is an example of periodic motion (or oscillatory motion). We will now give the definitions of some important terms connected with the pendulum. These are : length of pendulum, oscillations, time-period and amplitude.

(i) Length of Pendulum :

The length of thread from the point of suspension to the centre of bob, is called length of pendulum. The time-period of a pendulum depends on its length. As the length of a pendulum is increased, its time-period also increases. The time-period of a pendulum of given length is constant.

(ii) Oscillations :

One complete to-and-fro movement of the pendulum bob is called an oscillation. One oscillation can be counted starting from one of the extreme positions of the bob or from the mean position. For example, in Figure 15(b), the motion of pendulum bob from its extreme position B to C, and back to B is called one oscillation. The motion of bob from its mean position A to B, then from B to C, and back to A is also equal to one oscillation.

(iii) Time-Period :

The time taken by pendulum bob to make one complete oscillation is called time-period of the pendulum. For example, in Figure (b), the time taken by bob to travel from position B to C and back to B is the time-period of pendulum. The time taken by bob in going from position A to B, then from B to C, and back to A is also equal to time-period.

The time taken by one oscillation of a pendulum is quite short and hence cannot be measured accurately. So, to find the time taken by one oscillation (or time-period), we measure the time taken by a large number of oscillations. Dividing the total time by the total number of oscillations, we get the time for one oscillation (or time-period) of the pendulum.

For example, we can find the time for, say 20 oscillations of the pendulum by using a stop watch. This time divided by 20 will give us the time taken for one oscillation. That is, it will give the time-period of the pendulum.

(iv) Amplitude. As the pendulum oscillates (or swings) to-and-fro, the maximum displacement of the bob from its mean position on either side is called the amplitude of pendulum. In Figure (b), the distance AB is the amplitude of pendulum. The distance AC is also equal to amplitude of pendulum. Please note that whether the amplitude of oscillations of a pendulum is large or small, the time taken for one complete oscillation (or time-period) remains the same.

**Activity 2**

**To Determine the Time-Period of a Pendulum**

We can determine the time-period of a simple pendulum by performing an activity as follows: Set up a simple pendulum as shown in Figure (a) with a thread of length nearly 1 metre, carrying the bob at lower end and tied at its upper end from a rigid support (like an iron stand). Switch off the nearby fans so that they may not interfere with the oscillations of pendulum. We will need a stop watch (or stop clock) to measure the time- period of pendulum.

- To set the pendulum in motion, hold the bob gently and move it slightly to one side (say, right side). Make sure that the thread attached to bob remains taut when we displace it.
- Now release the bob from its displaced position gently. Do not push the bob while releasing it.
- Start the stop watch (or stop clock) when the bob is at one of the extreme positions. Keep on counting the number of oscillations made by the pendulum bob.
- Measure the time which pendulum bob takes to make 20 complete oscillations. Divide the time taken for 20 oscillations by 20. This will give us the time taken by pendulum for making one oscillation. It is the time-period of pendulum.

Suppose the time taken for 20 oscillations of the pendulum as measured by the stop watch is 48 seconds (see Figure). Then the time period of this pendulum will be \(\frac{48}{20}\) = 2.4 seconds (or 2.4 s).

Let us now solve one problem based on the calculation of time-period of a simple pendulum.

**Example Problem.**

A simple pendulum takes 32 s to complete 20 oscillations. What is the time-period of this pendulum ?

**Solution**:

Time taken for 20 oscillations = 32 s

So, Time taken for 1 oscillation = \(\frac{32 \mathrm{~s}}{20}\)

= 1.6 s

Thus, the time-period of this pendulum is 1.6 seconds.

The fact that the time-period of a given pendulum is constant was discovered by a scientist named Galileo Galilie just by chance. Once Galileo was sitting in a Church. He noticed that a lamp hanging from the ceiling with a long chain was swinging slowly from side to side (or oscillating).

Clocks and watches were not available at that time. So, Galileo used his pulse rate as a kind of watch. He was surprised to find that his pulse ‘beat’ the same number of times during the time interval in which the swinging lamp completed ‘one oscillation. This observation gave him the idea that the time-period of a given pendulum is constant.

Galileo then conducted experiments with various pendulums to verify his observations. He came to the conclusion that a pendulum of given length always takes the same time to complete one oscillation. In other words, the time-period of a pendulum of given length is constant.

This observation led to the development of pendulum clocks. Thus, the periodic motion of pendulum has been used to make pendulum clocks for measuring time. Please note that the pendulum used for making pendulum clocks is not the thread-type simple pendulum, it is an all metal pendulum.

### The Use of Pendulum for Measuring Time : Pendulum Clock

The periodic motion of a pendulum is utilised in pendulum clocks for measuring time. So, in a pendulum clock, the swinging pendulum regulates time. The pendulum of a ‘pendulum clock’ is a long metal rod having a heavy metal bob at its lower end (see Figure).

When the lower end of pendulum is displaced to one side and then released, the pendulum starts swinging left and right continuously (There is a mechanism in the pendulum clock which does not allow swinging pendulum to stop). Each swing (or oscillation) of the pendulum takes the same time. The pendulum clock uses this periodic motion of pendulum for measuring time.

Actually, when the pendulum swings continuously, its upper end drives some toothed wheels (which are connected to it by a suitable mechanism). The toothed wheels then turn the hours’ hand, minutes’ hand and seconds’, hand on the dial of the clock due to which we are able to read time. A pendulum clock is shown in Figure. The pendulum clocks are not used much these days.

The pendulum clocks were big and bulky, so they could not be carried everywhere easily. Pendulum clocks were usually kept fixed at a place and used for reading time. In order to make small, light and portable clocks and watches, a kind of modified pendulum was developed which is much smaller and compact than the traditional pendulum used in pendulum clocks.

It is called ‘balance wheel’ and ‘hair spring’ arrangement [see Figure(a)], A balance wheel connected to a hair spring shows periodic motion.

The inner end of hair spring is attached to the centre of balance wheel and the outer end of hair spring is fixed to the frame of a clock or watch [see Figure (a)], When the balance wheel is displaced slightly to one side and released, it starts oscillating back and forth continuously.

Each oscillation of balance wheel takes the same time. Till recently, most of the clocks and watches used the periodic motion of a balance wheel and hair spring arrangement for their working. These were called winding clocks and watches because they were run by winding a special kind of spring with the help of a winding key [see Figures (b) and (c)]. Even the winding type clocks and watches are not used much these days. They have been replaced by quartz clocks and watches.

### The Latest Trend in Measurement of Time : Use of Quartz Crystals

Quartz is a hard mineral consisting of silica. These days, the regular oscillations (or vibrations) of a tiny quartz crystal (when joined into an electric circuit), are used for measuring time very accurately. So, most of the accurate clocks and watches these days use quartz crystals for measuring time.

The clocks and watches which use quartz crystals for their working are called quartz clocks and quartz watches. They are also called electronic clocks and watches. The time measured by quartz clocks and watches is much more accurate than that measured by clocks and watches which were available earlier.

Thus, very accurate measurement of time is now possible by using quartz clocks and watches. The quartz clocks and watches (or electronic clocks and watches) can be of two types : non-digital and digital.

The non-digital quartz clocks and watches are just like traditional clocks and watches having hours’, minutes’ and seconds’ hands which move on a dial [see Figure (a)]. The digital quartz clocks and watches do not have the traditional hours’, minutes’ and seconds’ hands.

These clocks and watches display time directly in digits [see Figure (b)], Quartz clocks and watches require electric cells for their working. The very accurate measurement of time is also done by using atomic clocks which make use of the regular oscillations (or vibrations) of individual atoms for their time keeping.

The smallest time interval that can be measured with commonly available clocks and watches is 1 second. Special clocks and watches are, however, now available which can measure time intervals much smaller than a second accurately.

The clocks and watches used in sports meets can measure time intervals that are one-tenth of a second or one-hundredth of a second. There are some clocks which can measure time intervals as small as microsecond or even a nanosecond. Clocks which measure such small time intervals are used for scientific research.