. A simple pendulum oscillates, the amplitude of oscillation is reduced to one third of its initial amplitude A, at the ends of 10 oscillations. After complete 20 oscillations, its amplitude must be?

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. A simple pendulum oscillates, the amplitude of oscillation is reduced to one third of its initial amplitude A, at the ends of 10 oscillations. After complete 20 oscillations, its amplitude must be?

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. A simple pendulum oscillates, the amplitude of oscillation is reduce...

Introduction:
A simple pendulum is a system consisting of a mass (bob) attached to a fixed point by a string or rod. It exhibits periodic oscillatory motion, where the amplitude is the maximum displacement of the bob from its equilibrium position. This question asks us to determine the amplitude of the pendulum after 20 oscillations, given that its amplitude is reduced to one-third of its initial amplitude after 10 oscillations.

Understanding the problem:
We are given that the amplitude of the pendulum is reduced to one-third of its initial amplitude after 10 oscillations. This implies that the amplitude decreases with each oscillation. We need to find the amplitude after 20 oscillations.

Approach:
To solve this problem, we can use the concept of damping in simple harmonic motion. Damping refers to the gradual loss of energy in a system, causing the amplitude to decrease over time. We can assume that the pendulum experiences damping, leading to a decrease in amplitude.

Step 1: Determining the reduction factor:
Let's assume the initial amplitude of the pendulum is A. After 10 oscillations, the amplitude is reduced to one-third of A. This means the new amplitude is A/3.

Step 2: Determining the reduction per oscillation:
To determine the reduction per oscillation, we can divide the reduction factor by the number of oscillations. In this case, the reduction per oscillation is (A - A/3) / 10.

Step 3: Applying the reduction per oscillation:
To find the amplitude after 20 oscillations, we can apply the reduction per oscillation twice. The amplitude after 20 oscillations is given by A - 2 * (A - A/3) / 10.

Step 4: Simplifying the expression:
Simplifying the expression, we get A - (2/10) * (A - A/3) = A - (A - A/3)/5.

Step 5: Calculating the final amplitude:
To calculate the final amplitude, we can simplify the expression further: A - (A - A/3)/5 = (5A - (A - A/3))/5 = (5A - A + A/3)/5 = (7A/3)/5 = 7A/15.

Conclusion:
Therefore, after 20 oscillations, the amplitude of the pendulum will be 7A/15, where A is the initial amplitude.

Answered by Mohit Rajpoot · View profile

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Attempt All sub parts from each question.Damping: When an analog instrument is used to measure a physical parameter, a deflecting torque is applied to the moving system which is deflected from its initial position and should move steadily to the deflected position. But due to inertia, the moving system keeps on oscillating about equilibrium. To remove the oscillation of the moving system a damping torque is required. The damping torque should be of such that the pointer quickly comes to its final steady position, without overshooting. If the instrument is underdamped, the moving system will oscillate about the final steady position with a decreasing amplitude and will take some time before it comes to rest. When the moving system moves rapidly but smoothly to its final steady position, the instrument is said to be critically damped or deadbeat. If the damping torque is more than what is required for critical damping, the instrument is said to be overdamped. In an overdamped instrument, the moving system moves slowly to its final steady position in a lethargic fashion.Methods of producing damping torque:(i) Air friction damping(ii) Fluid friction damping(iii) Eddy current dampingAir Friction Damping: A light piston is attached to the moving system. This piston moves in an air chamber closed at one end. When there is an oscillation, the piston moves in and out of the chamber. When the piston moves into the chamber, the air inside is compressed and an air pressure is built up which opposes the motion of the piston and thus the moving system faces a damping torque which ultimately reduces the oscillation. Fluid Friction Damping: In this type of damping oil is used in place of air. Viscosity of the oil being greater, the damping torque is also more. A disc is attached to the moving system which is completely dipped into the oil. When the moving system oscillates, the disc moves in oil and a frictional drag is produced. This frictional drag opposes the oscillation. Eddy Current Damping: The moving system is connected to an aluminium disc which rotates in a magnetic field. Rotation in magnetic field induces an emf in it and if the path is closed, a current (known as eddy current) flows. This current interacts with the magnetic field to produce an electromagnetic torque which opposes the motion. This torque is proportional to the oscillation of the moving system. This electromagnetic torque ultimately reduces the oscillation. Air friction damping provides a very simple and cheap method of damping. The disadvantages of fluid friction damping are that it can be used only for instruments which are in vertical position. Eddy current damping is the most efficient form of damping.Q. The most efficient form of damping is

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Attempt All sub parts from each question.Damping: When an analog instrument is used to measure a physical parameter, a deflecting torque is applied to the moving system which is deflected from its initial position and should move steadily to the deflected position. But due to inertia, the moving system keeps on oscillating about equilibrium. To remove the oscillation of the moving system a damping torque is required. The damping torque should be of such that the pointer quickly comes to its final steady position, without overshooting. If the instrument is underdamped, the moving system will oscillate about the final steady position with a decreasing amplitude and will take some time before it comes to rest. When the moving system moves rapidly but smoothly to its final steady position, the instrument is said to be critically damped or deadbeat. If the damping torque is more than what is required for critical damping, the instrument is said to be overdamped. In an overdamped instrument, the moving system moves slowly to its final steady position in a lethargic fashion.Methods of producing damping torque:(i) Air friction damping(ii) Fluid friction damping(iii) Eddy current dampingAir Friction Damping: A light piston is attached to the moving system. This piston moves in an air chamber closed at one end. When there is an oscillation, the piston moves in and out of the chamber. When the piston moves into the chamber, the air inside is compressed and an air pressure is built up which opposes the motion of the piston and thus the moving system faces a damping torque which ultimately reduces the oscillation. Fluid Friction Damping: In this type of damping oil is used in place of air. Viscosity of the oil being greater, the damping torque is also more. A disc is attached to the moving system which is completely dipped into the oil. When the moving system oscillates, the disc moves in oil and a frictional drag is produced. This frictional drag opposes the oscillation. Eddy Current Damping: The moving system is connected to an aluminium disc which rotates in a magnetic field. Rotation in magnetic field induces an emf in it and if the path is closed, a current (known as eddy current) flows. This current interacts with the magnetic field to produce an electromagnetic torque which opposes the motion. This torque is proportional to the oscillation of the moving system. This electromagnetic torque ultimately reduces the oscillation. Air friction damping provides a very simple and cheap method of damping. The disadvantages of fluid friction damping are that it can be used only for instruments which are in vertical position. Eddy current damping is the most efficient form of damping.Q. In Fluid Friction Damping the amount of damping torque

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Attempt All sub parts from each question.Damping: When an analog instrument is used to measure a physical parameter, a deflecting torque is applied to the moving system which is deflected from its initial position and should move steadily to the deflected position. But due to inertia, the moving system keeps on oscillating about equilibrium. To remove the oscillation of the moving system a damping torque is required. The damping torque should be of such that the pointer quickly comes to its final steady position, without overshooting. If the instrument is underdamped, the moving system will oscillate about the final steady position with a decreasing amplitude and will take some time before it comes to rest. When the moving system moves rapidly but smoothly to its final steady position, the instrument is said to be critically damped or deadbeat. If the damping torque is more than what is required for critical damping, the instrument is said to be overdamped. In an overdamped instrument, the moving system moves slowly to its final steady position in a lethargic fashion.Methods of producing damping torque:(i) Air friction damping(ii) Fluid friction damping(iii) Eddy current dampingAir Friction Damping: A light piston is attached to the moving system. This piston moves in an air chamber closed at one end. When there is an oscillation, the piston moves in and out of the chamber. When the piston moves into the chamber, the air inside is compressed and an air pressure is built up which opposes the motion of the piston and thus the moving system faces a damping torque which ultimately reduces the oscillation. Fluid Friction Damping: In this type of damping oil is used in place of air. Viscosity of the oil being greater, the damping torque is also more. A disc is attached to the moving system which is completely dipped into the oil. When the moving system oscillates, the disc moves in oil and a frictional drag is produced. This frictional drag opposes the oscillation. Eddy Current Damping: The moving system is connected to an aluminium disc which rotates in a magnetic field. Rotation in magnetic field induces an emf in it and if the path is closed, a current (known as eddy current) flows. This current interacts with the magnetic field to produce an electromagnetic torque which opposes the motion. This torque is proportional to the oscillation of the moving system. This electromagnetic torque ultimately reduces the oscillation. Air friction damping provides a very simple and cheap method of damping. The disadvantages of fluid friction damping are that it can be used only for instruments which are in vertical position. Eddy current damping is the most efficient form of damping.Q. When the moving system of a measuring instrument moves rapidly but smoothly to its final steady position, the instrument is said to be

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. A simple pendulum oscillates, the amplitude of oscillation is reduced to one third of its initial amplitude A, at the ends of 10 oscillations. After complete 20 oscillations, its amplitude must be?

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. A simple pendulum oscillates, the amplitude of oscillation is reduced to one third of its initial amplitude A, at the ends of 10 oscillations. After complete 20 oscillations, its amplitude must be? for Class 11 2024 is part of Class 11 preparation. The Question and answers have been prepared according to the Class 11 exam syllabus. Information about . A simple pendulum oscillates, the amplitude of oscillation is reduced to one third of its initial amplitude A, at the ends of 10 oscillations. After complete 20 oscillations, its amplitude must be? covers all topics & solutions for Class 11 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for . A simple pendulum oscillates, the amplitude of oscillation is reduced to one third of its initial amplitude A, at the ends of 10 oscillations. After complete 20 oscillations, its amplitude must be?.

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