Simple pendulum and time period

Parts of a simple pendulum

A simple pendulum is a small metal ball, called the bob, hung from a rigid support by a long thread. When the bob hangs still, straight down, it is at its mean position (O). Move the bob slightly to one side and let it go: it swings to and fro. This motion is periodic, because the bob repeats its path after a fixed interval of time. It is the same kind of oscillatory motion as an eraser swinging on a thread, which you may have seen in Class 6.

One oscillation and the time period

The farthest points of the swing are the extreme positions, A and B. The bob completes one oscillation when it starts at O, moves to A, turns back, swings to B, turns again and returns to O. Going from A to B and back to A is also one oscillation. The time taken for one oscillation is the time period of the pendulum.

Measure it yourself

Tie a heavy ball or stone to a string about 150 cm long and fix the string to a rigid support so that about 100 cm hangs between the support and the bob. Wait for the bob to rest, then move it slightly to one side and release it gently, without a push and with the string taut. Time 10 oscillations with a watch, repeat 3 or 4 times, and divide each time by 10.

Trial	Time for 10 oscillations → time period (sample)
1	20.1 s → 2.01 s
2	19.9 s → 1.99 s
3	20.0 s → 2.00 s

The time period comes out almost the same every time. Your readings may differ a little from these sample values, but they should agree closely with one another.

What changes the time period?

Think like a scientist and test one change at a time. Keep the same bob and use threads of two or three different lengths: the longer the pendulum, the longer its time period. Then keep the length fixed and change the bob for a lighter or heavier one: the time period stays the same. So the time period of a simple pendulum depends on its length but not on the mass of the bob, and all pendulums of the same length have the same time period at a given place. (Extra: the sample values in the picture, about 1.0 s for 25 cm, 1.4 s for 50 cm and 2.0 s for 100 cm, show that making a pendulum four times as long doubles its time period.)

Galileo and Huygens

It is said that Galileo Galilei (1564–1642), sitting in a church, noticed a hanging lamp swinging back and forth. Using his own pulse as a timer, he found that each swing took the same time. After experimenting with different pendulums, he concluded that a pendulum of a given length always takes the same time for one oscillation. Inspired by this, Christiaan Huygens (1629–1695) invented the pendulum clock in 1656 and patented it in 1657.

Why it matters

Because the time period of a pendulum of fixed length stays constant, its swings can count equal intervals of time, the basic idea behind every clock. You can see the same physics on a playground swing, whose time period also depends on its length. Read how pendulums fit into the history of clocks in how is time measured. Answers to the textbook questions are in the NCERT solutions for Chapter 8; see all of Chapter 8 notes.