A question about Vibrations....

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In summary, there is a misconception about a "full cycle" for a vibrating pendulum. A full cycle includes the pendulum swinging to the left, back to center, to the right, and back to center. Damping does not affect this definition of a full cycle. However, for a dampened oscillation, the amplitude decreases with time and there is a period of oscillation between minimum or maximum displacement, meaning it does not return to its original state. Therefore, there is no complete cycle for a dampened oscillation according to the traditional definition.
  • #1
Kaneki123
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Okay...I just have a simple question...For a vibrating pendulum, a one complete cycle is considered when it displaces from a certain position A and then again returns to that certain position A...My question is that the damping is continuosly taking place on the pendulum, so there is no way that the pendulum is returning exactly at that same point, so is there a problem in my assumption or "one complete cylce or one complete vibration" is all theoretical?
 
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  • #2
You appear to have some misconception about a "full cycle." Imagine that we begin to measure the cycle from the vertical, and the pendulum first swings to the left, then back to the center, then to the right, and finally back to the center. A full cycle takes in all the motion just described. Your description sounded more like a half cycle.

Regarding damping, and again starting from the vertical, the pendulum swings left, then back to center, then to the right, then back to center, and all of this remains true, with, or without, damping. It passes repeatedly through the center, so it most definitely returns to that point.
 
  • #3
Technically speaking, there is no complete cycle for a dampened oscillation if your definition for a cycle requires that the system returns to its original state. However, there is an amplitude that decreases with time and a period of oscillation between minimum or maximum displacement.

AM
 

1. What are vibrations?

Vibrations refer to the back-and-forth or up-and-down movements of an object or medium. These movements are caused by the transfer of energy from one point to another.

2. What are the different types of vibrations?

There are three main types of vibrations: free, forced, and damped. Free vibrations occur when an object vibrates on its own without any external force. Forced vibrations occur when an external force is applied to an object, causing it to vibrate. Damped vibrations occur when an object's vibrations are gradually reduced by a resisting force, such as friction.

3. What causes vibrations?

Vibrations can be caused by a variety of factors, including mechanical forces, sound waves, and electrical signals. For example, a vibrating phone is caused by electrical signals from a call or message, while a guitar string vibrates due to the mechanical force from strumming.

4. How are vibrations measured?

Vibrations are measured using instruments called accelerometers. These devices measure the acceleration of an object or medium, which can be used to determine the frequency and amplitude of vibrations. Other methods of measuring vibrations include laser vibrometry and strain gauges.

5. What are the practical applications of understanding vibrations?

Understanding vibrations is important in various fields, including engineering, physics, and music. It allows for the design and improvement of structures and machines to prevent unwanted vibrations, as well as the creation of musical instruments and sound systems. Vibrations are also used in medical imaging techniques, such as ultrasound, to diagnose and treat medical conditions.

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