How Does Damping Force Relate to Velocity in a Pendulum?

[jrm2002]

Damping Regarding Damping!

Let us say we have a have mass concentrated at the end of a string(simple pendulum).Let us say the pendlum is set in motion and then eventually due to energy loss through air resistance, the amplitude of the oscillation will reduce and eventually the pendulum comes to rest.

These damping forces are taken in problems as:

Damping force=(Damping Coefficient) x velocity of vibration

My questions are:
1. how is the damping force proportional to velocity of vibration?
2. What is this damping coefficient?What does the damping coefficient physically denote??

 

[berkeman]

-1- That's an approximation -- for example, what can you say about air resistance and velocity? What happens to air resistance as you go faster in a car?

-2- Do you have a feeling for what "damping" means? It's how quickly the oscillation is quenched. Think of a guitar string. When you pluck the string, it takes a few seconds to stop oscillating (low damping), right? You can stop that oscillation faster if you grab the string hard (high damping), or you can control the fade of the sound by touching the string lightly (medium damping).

 

[kyle8921]

1. The damping force is proportional to the velocity of vibration because the faster the pendulum is moving, the more air resistance it encounters, resulting in a larger damping force. This relationship is described by the equation for damping force, where the damping coefficient is a constant that determines the strength of the damping force.

2. The damping coefficient is a measure of the strength of the damping force. It physically denotes the amount of energy that is dissipated per unit of velocity. A higher damping coefficient means that more energy is being lost per unit of velocity, resulting in a faster decrease in amplitude and a faster return to rest. This coefficient can vary depending on factors such as the shape and size of the object, the medium it is moving through, and any other external forces acting on the object.