state the laws of a simple pendulum.
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1. The first law of the simple pendulum states that the period of oscillation of a simple pendulum of constant length is independent of its amplitude, provided the amplitude is small.
Let us conduct an activity to verify the first law of the simple pendulum. To verify the first law, the apparatus required are a metallic bob, a thin and strong thread of length around 120 cm, an iron stand with a clamp, a cork vertically cut into two parts, a metre scale and a stop watch. Place the iron stand over a table. Tie the metallic bob to the thread and suspend it from the stand with the help of the cork and clamp. The simple pendulum is set up.
Choose a length for the pendulum, say 50 cm. Pull the bob to a side such that the amplitude is about 10 cm and allow the pendulum to oscillate. When the bob is at one of the extreme positions, start the stop watch. Count 20 oscillations and stop the stop watch. Note the time taken for 20 oscillations. Calculate the time taken for one oscillation, which is the time period of oscillation. Now repeat the procedure with amplitudes 15 cm and 20 cm. Don’t change the length of the pendulum. Then tabulate the readings. We will observe that the time period of oscillation remains the same for different amplitudes. Thus, the period of oscillation is independent of amplitude, provided the amplitudes are small. This verifies the first law.
2. The second law of the simple pendulum states that the period of oscillation of a simple pendulum of constant length is independent of the size, shape, mass and material of the bob, provided it is not very light, such as cork. Let us verify the second law of the simple pendulum. Take three bobs of different masses and different materials. Set up a simple pendulum with the first bob for a fixed length, say 50 cm. Choose an amplitude, say 5 cm and pull the bob to a side. Now release the bob and make it to oscillate. Start the stop watch when the bob is at one of its extreme positions. Count 20 oscillations and stop the stop watch. Note the time taken for 20 oscillations. Calculate the time taken for one oscillation, which gives the time period of simple pendulum. Tabulate the readings. Now repeat the procedure with the second bob and the third bob by keeping the length of the pendulum and the amplitude the same. Then tabulate the readings. It will be observed that the period of oscillation does not change with the mass and material of the bob, provided the length of the pendulum and amplitude are constant. This verifies the second law.
3. The third law of the simple pendulum states that the time period of oscillation of a simple pendulum is directly proportional to the square root of the length of the pendulum, for a given place. That is,
T α √L. --------------(1)
Equation (1) can be written as
√L/T = constant
On squaring the equation, we get
L/T2 = constant
Let us now verify the third law of the simple pendulum. Set up the pendulum with a metallic bob as in the experiment to verify the first law. Select a length, say 50 cm. Pull the bob to a side such that the amplitude of the pendulum is not greater than 5 cm and release it. The pendulum starts oscillating. Start the stop watch when the bob is at one of its extreme positions. Count 20 oscillations and stop the stop watch. Note the time taken for 20 oscillations and tabulate the readings under the head trial-one. Repeat the procedure with the same length and amplitude. Note the time taken for 20 oscillations and tabulate the readings under the heads trial-two and trial-three , and so on. Calculate the average time taken for 20 oscillations and determine the time taken for one oscillation. Then tabulate all the readings. Now find the value of L by T square for the given length of the pendulum. Now increase the length of the pendulum by about 10 cm and repeat the procedure to find the value of L/T2. Repeat the procedure three or four times by increasing the length of the pendulum by 10 cm every time. Now tabulate the readings. It will be observed that the time period of the pendulum increases with its length, and the value of L/T2 is the same in all the cases. This verifies the third law.
Let us conduct an activity to verify the first law of the simple pendulum. To verify the first law, the apparatus required are a metallic bob, a thin and strong thread of length around 120 cm, an iron stand with a clamp, a cork vertically cut into two parts, a metre scale and a stop watch. Place the iron stand over a table. Tie the metallic bob to the thread and suspend it from the stand with the help of the cork and clamp. The simple pendulum is set up.
Choose a length for the pendulum, say 50 cm. Pull the bob to a side such that the amplitude is about 10 cm and allow the pendulum to oscillate. When the bob is at one of the extreme positions, start the stop watch. Count 20 oscillations and stop the stop watch. Note the time taken for 20 oscillations. Calculate the time taken for one oscillation, which is the time period of oscillation. Now repeat the procedure with amplitudes 15 cm and 20 cm. Don’t change the length of the pendulum. Then tabulate the readings. We will observe that the time period of oscillation remains the same for different amplitudes. Thus, the period of oscillation is independent of amplitude, provided the amplitudes are small. This verifies the first law.
2. The second law of the simple pendulum states that the period of oscillation of a simple pendulum of constant length is independent of the size, shape, mass and material of the bob, provided it is not very light, such as cork. Let us verify the second law of the simple pendulum. Take three bobs of different masses and different materials. Set up a simple pendulum with the first bob for a fixed length, say 50 cm. Choose an amplitude, say 5 cm and pull the bob to a side. Now release the bob and make it to oscillate. Start the stop watch when the bob is at one of its extreme positions. Count 20 oscillations and stop the stop watch. Note the time taken for 20 oscillations. Calculate the time taken for one oscillation, which gives the time period of simple pendulum. Tabulate the readings. Now repeat the procedure with the second bob and the third bob by keeping the length of the pendulum and the amplitude the same. Then tabulate the readings. It will be observed that the period of oscillation does not change with the mass and material of the bob, provided the length of the pendulum and amplitude are constant. This verifies the second law.
3. The third law of the simple pendulum states that the time period of oscillation of a simple pendulum is directly proportional to the square root of the length of the pendulum, for a given place. That is,
T α √L. --------------(1)
Equation (1) can be written as
√L/T = constant
On squaring the equation, we get
L/T2 = constant
Let us now verify the third law of the simple pendulum. Set up the pendulum with a metallic bob as in the experiment to verify the first law. Select a length, say 50 cm. Pull the bob to a side such that the amplitude of the pendulum is not greater than 5 cm and release it. The pendulum starts oscillating. Start the stop watch when the bob is at one of its extreme positions. Count 20 oscillations and stop the stop watch. Note the time taken for 20 oscillations and tabulate the readings under the head trial-one. Repeat the procedure with the same length and amplitude. Note the time taken for 20 oscillations and tabulate the readings under the heads trial-two and trial-three , and so on. Calculate the average time taken for 20 oscillations and determine the time taken for one oscillation. Then tabulate all the readings. Now find the value of L by T square for the given length of the pendulum. Now increase the length of the pendulum by about 10 cm and repeat the procedure to find the value of L/T2. Repeat the procedure three or four times by increasing the length of the pendulum by 10 cm every time. Now tabulate the readings. It will be observed that the time period of the pendulum increases with its length, and the value of L/T2 is the same in all the cases. This verifies the third law.
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