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| Forces Acting on the Bob of a Simple Pendulum |
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| The bob of a simple pendulum is attached to a string which pulls the bob along its length. |
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| Bob of a simple pendulum attached to a string |
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| When the bob is at the extreme position B, the string pulls it along (BO) and the Earth pulls the bob vertically downwards. Since the string and the Earth are pulling the bob in the opposite directions, the two forces cannot balance each other. As a result the bob moves along the dotted line as shown in the above figure. The speed of the bob increases as it approaches the mean position A and continues to move till it reaches C. At C the speed becomes zero and due to the unbalanced force the bob moves towards the mean position. The speed of the bob is maximum at the mean position and is zero at the extreme positions. |
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| Law of conservation of energy holds good in the case of a simple pendulum. As the bob is displaced to one end, it gains potential energy and as it is released from rest, it starts gaining kinetic energy till it reaches the mean position. Kinetic energy possessed by the pendulum is maximum at the mean position and zero at the extreme positions, whereas the potential
energy is maximum at the extreme positions and is zero at the mean position. At intermediate positions, the energy is partly kinetic and partly potential. |
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| If you watch an oscillating pendulum for a long time you will find that the amplitude of oscillations gradually decreases. Suppose the bob of the pendulum reaches up to B while oscillating, then AB is the amplitude. For the next oscillation the bob fails to reach B but it will reverse the direction from point B| instead of B. The amplitude of oscillation in the second case is AB| which is less than AB. That means, a retarding force is acting on the bob thereby reducing the amplitude of oscillation. This retarding force is nothing but air-resistance or air-friction. This force of friction gradually decreases the amplitude of oscillation and the bob finally stops oscillating. This decrease in amplitude as time passes is known as “Damping of oscillations”. If air is removed, the oscillations will continue for a much longer time. Thus, we know that three forces are acting on the pendulum and they are: |
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 the pull of the string |
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 the force of gravity and |
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 the air resistance |
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| Damping of oscillations is sometimes desirable and helpful. |
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| For instance: |
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 weighing with a spring balance or a pan balance is possible due to damping of the oscillations otherwise it would not have been possible to read the scale. |
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 shock absorbers in an automobile help in the damping of oscillations due to unevenness of road. |
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| When a simple pendulum oscillates, the bob of the pendulum comes back to the mean position from the extreme positions by the force of gravity and pull of the string. That is, the simple pendulum is restored to its equilibrium position by these forces and such forces are described as restoring forces. |
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| The force which tends to bring the body on which it is acting, towards its mean position is called Restoring force. |
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| 1) Find the length of a simple pendulum whose time period is 6.28
s. |
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| Time period T = 6.28 s. |
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| Length of the pendulum = 9.8 m |
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| 2) Time taken by a simple pendulum to execute 20 oscillations is 28 s. What is the time period? |
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| Time taken to execute 20 oscillations = 28 s. |
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| Time period of the pendulum = 1.4 s |
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| 3) Find the length of a pendulum whose
time period is 1 s.? |
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| Time period (T) = 1 s. |
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| Length of the pendulum = 0.248 cm |
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 Oscillatory motion or harmonic motion is a type of motion in which the to and fro motion of the object repeats itself at regular intervals of time about the mean position. |
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 Simple Pendulum consists of a heavy mass (spherical in shape) suspended by a long, inextensible and flexible string from a point about which it can oscillate. |
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 Length of the pendulum is the distance from the point of suspension to the bob. |
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 Amplitude of the pendulum is the distance covered by the bob from the mean position to an extreme position. |
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 Restoring force is that force which tends to bring the body on which it is acting, towards its mean position. |
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