# Frequency and viscous friction in a spring?

• nothGing
In summary, the relationship between frequency and viscous friction in a spring involves considering the damping effect and modeling it as proportional to velocity in a damped oscillator. The frequency itself does not affect the friction force, but it does impact the power delivered to the liquid. With knowledge of the spring constant and frequency, the ODE can be solved to find the velocity in terms of displacement.
nothGing
Hi.
may i ask the relationship(formula) between frequency and viscous friction in a spring?

are you talking about hookes law F=-Kx
And the angular frequency would be w=square root of k/m

your equation is right if not consider the viscous friction, but since it must consider the friction, so how arh?

In a damped oscillator the resistance is just modeled as proportional to velocity. The frequency has nothing to do with the friction force, it will just increase power delivered to the liquid.

If you know spring constant and frequency, then you can find v(x) by solving the ODE. I guess that's what you're asking.

Hello,

The relationship between frequency and viscous friction in a spring can be described by the following formula:

f = (1/2π) * √(k/m) * (1 - ζ^2)^1/2

Where:
f = frequency of the spring's oscillations
k = spring constant
m = mass attached to the spring
ζ = viscous damping coefficient

This formula shows that as the frequency of the spring's oscillations increases, the viscous friction also increases. This is because higher frequencies result in more rapid and frequent movements of the spring, causing more energy to be dissipated through friction.

Additionally, the presence of viscous friction in a spring can also affect its natural frequency, or the frequency at which it will oscillate without any external forces. Viscous friction can decrease the natural frequency of a spring, making it oscillate at a slower rate.

I hope this helps to answer your question. Let me know if you have any further inquiries.

Best,

## 1. What is frequency in relation to a spring?

Frequency, in the context of a spring, refers to the rate at which the spring oscillates or vibrates. It is measured in Hertz (Hz) and is affected by factors such as the mass of the object attached to the spring and the stiffness of the spring itself.

## 2. How does the frequency of a spring change with different masses?

The frequency of a spring is inversely proportional to the square root of the mass attached to it. This means that as the mass increases, the frequency decreases, and vice versa.

## 3. How does viscous friction impact the behavior of a spring?

Viscous friction, also known as damping, is a force that opposes the motion of a spring. It causes the amplitude of the oscillations to decrease over time, resulting in a decrease in the frequency of the spring. Viscous friction can also cause the spring to eventually come to rest.

## 4. Can the stiffness of a spring affect its frequency?

Yes, the stiffness of a spring directly affects its frequency. A stiffer spring will have a higher frequency, while a more flexible spring will have a lower frequency. This is because the stiffer spring requires more force to produce the same amount of displacement, resulting in a faster oscillation.

## 5. How can frequency and viscous friction in a spring be measured?

The frequency of a spring can be measured by attaching a mass to the spring and measuring the period of its oscillations (the time it takes to complete one full cycle). Viscous friction can be measured by observing the decrease in amplitude of the oscillations over time. Both of these can also be calculated using mathematical formulas based on the properties of the spring and the attached mass.

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