##### The time-period of a simple pendulum

The time-period of a simple pendulum :

1. Depends on Length of pendulum, L

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2. Depends on Acceleration due to gravity, g

3. Does not depend on the mass of the bob

4. Does not depend on the amplitude of oscillations

* The time-period of a simple pendulum is directly propotional to the square root of its length.

Thus, wen de length of pendulum is made 4 times, then de period will become 2 times, i.e., it’ll get doubled. And if the length of a simple pendulum is made one-fourth. Then it time-period will become half, i.e., it will get halved. Thus, as de length of de pendulum is increased, its time-period also increases.

And wen de length of de pendulum is decreased, its time-period also decreases. In summer, a pendulum clock runs late because in hot weather de pendulum expands ; its length increases. Due to increase in length of pendulum, its time-period increases. The pendulum swings more slowly and the clock loses time.

* The time-period of a simple pendulum is inversely propotional to the square root of de acceleration due 2 gravity at tat place.

For example, the value of g on de moon is less that that on the earth. So, the time-period of the same pendulum will be more on the moon ; less on the earth.

* To show that the period of a pendulum does not depend on the Mass of Bob.

We take a number of bobs of different masses and, keeping the length of pendulum constant, we measure the time taken for 20 oscillations with each bob. Knowing the time for 20 oscillations, the time for 1 oscillation can be found in each case. In one such experiment, the following observations were obtained (the length of pendulum being kept constant at 1 metre ) :

Mass of the bob

Time for 20 oscillations

Time for 1 oscillation (Time – period, T)

5 g

40.2 s

2.01 s

10 g

40.2 s

2.01 s

15 g

40.2 s

2.01 s

20 g

40.2 s

2.01 s

25 g

40.2 s

2.01 s

From the above table we find that even if we use bobs of different masses like 5g, 10 g, 15g, 20g, 24g, etc., the taken for 1 oscillation of pendulum does not change. It remains the same 2.01 seconds. From this we conclude that the time- period of pendulum does not depend on the mass of the pendulum bob.

* To show the Dependence Of period of pendulum on its length:

In an experiment using the same bob, but different lengths of the pendulum, the following observations were obtained:

Length of Pendulum (L)

Time for 20 oscillations

Time for 1 oscillation

(Time – period)

25 cm

20.1 s

1.005 s

36 cm

2401 s

1.205 s

49 cm

28.1 s

1.405 s

64 cm

32.2 s

1.610s

81 cm

36.2 s

1081 s

100 CM

40.2 S

2.0 S

From the above table we find that as the length of the pendulum increases from 25cm to 100cm, its time period increases from 1.005seconds to 2.01 seconds. From this we conclude that as the length of the simple pendulum is increased, its period also increases. It is, however, very important to note that the increase in time period is not proportional to increase in length. This because when we increase the length 4 times, then the increase in time period is only two times and not 4 times as required in the proportional relationship.

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