Chapter 2: Problem 70

What is a simple pendulum? Explain the terms time period, mean position and extreme positions of a simple pendulum.

Short Answer

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Answer: A simple pendulum consists of a small object called the pendulum bob, suspended by a low-mass, unstretchable string from a fixed support. Key concepts related to a simple pendulum include time period, mean position, and extreme positions. The time period is the duration for one complete oscillation, while the mean position is the equilibrium point where the bob has zero displacement. Extreme positions are the farthest points of the bob's oscillation, where kinetic energy is converted into potential energy. The pendulum oscillates back and forth from one extreme position to another, under the influence of gravity.

Step by step solution

Definition of a Simple Pendulum

A simple pendulum consists of a small object (called the pendulum bob) suspended by a low-mass, unstretchable string (called the rod) from a fixed support. When the bob is displaced from its equilibrium position and released, it oscillates back and forth in a regular periodic motion under the influence of gravity.

Time Period of a Simple Pendulum

The time period is the time taken for the pendulum to complete one full oscillation, i.e., to move from its initial position, reach the extreme position on the other side, and then return back to its initial position. The time period of a simple pendulum (T) can be represented mathematically using the formula: T = 2 \pi \sqrt{\frac{l}{g}}, where 'l' represents the length of the pendulum's rod and 'g' represents the acceleration due to gravity.

Mean Position of a Simple Pendulum

The mean or equilibrium position is the position where the pendulum bob would come to rest when there are no external forces acting upon it, other than gravity. It is the midpoint of the pendulum's motion, where the gravitational force acting on the bob is equal and opposite to the tension in the rod. When the bob is in its mean position, it has zero displacement, and all its potential energy is converted into kinetic energy.

Extreme Positions of a Simple Pendulum

Extreme positions are the points farthest away from the mean position on either side of the pendulum's oscillation path. At these points, the pendulum bob comes to a momentary stop, and all its kinetic energy is converted into potential energy. The extreme positions can also be referred to as the amplitude of the oscillation, which is the maximum displacement from the mean position.

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What is a simple pendulum? Explain the terms time period, mean position and extreme positions of a simple pendulum.

Short Answer

Step by step solution

Definition of a Simple Pendulum

Time Period of a Simple Pendulum

Mean Position of a Simple Pendulum

Extreme Positions of a Simple Pendulum

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