# Damping Constant: Solving for b Homework

In summary, the conversation discusses solving for the damping constant (b) in a system where the amplitude has decreased to 80% of its original height after 10 oscillations. The given equations do not feature a damping constant and a different formula may be needed to solve for it.

## Homework Statement

I am solving for the damping constant (b). The amplitude has decreased to 80% of its original height (0.1m) after 10 oscillations. The mass is 2 kg, k is 5000 N/m, w is 50 rads/s, T = pi/25 s.

x = 0.1cos(50t)
v = -5sin(50t)
a = -250cos(50t)

## The Attempt at a Solution

I am not sure what equation to use, I tried
w = ((k/m)-(b^2/4(m)^2))^1/2

Helo Tyler,

With those equations you'll never be able to solve for the damping constant -- it doesn't appear !
Where do you think it should be sitting ?

BvU said:
Helo Tyler,

With those equations you'll never be able to solve for the damping constant -- it doesn't appear !
Where do you think it should be sitting ?
I'm not sure, the answer in the back of the book is 0.71 kg/s. I think that I might need to use a different formula, but I'm not sure.

What I meant is that your relevant equations feature a constant amplitude: no damping.

BvU said:
What I meant is that your relevant equations feature a constant amplitude: no damping.
Those are the equations assuming no damping. Maybe they aren't relative...

I am solving for the damping constant (b). The amplitude has decreased to 80% of its original height (0.1m) after 10 oscillations
So you can not use ##x = 0.1\cos(50t)## . The link I gave you should help you further...

## 1. What is a damping constant?

A damping constant, also known as the damping coefficient or damping factor, is a parameter used in mathematical models to describe the rate at which a system loses energy. It is denoted by the letter b and is typically measured in units of force per velocity.

## 2. How is the damping constant related to the motion of a system?

The damping constant is directly related to the motion of a system by affecting the rate at which the system's oscillations decrease over time. A higher damping constant means that the system will lose energy more quickly, resulting in smaller oscillations and a quicker return to equilibrium.

## 3. What is the formula for calculating the damping constant?

The formula for calculating the damping constant varies depending on the type of system being modeled. For example, for a damped harmonic oscillator, the damping constant can be calculated using the formula b = 2 * (mass * damping ratio * natural frequency), where the damping ratio is a dimensionless value between 0 and 1.

## 4. How is the damping constant used in solving for motion equations?

The damping constant is used in solving for motion equations by incorporating it into the differential equations that describe the system's motion. By solving these equations, we can determine the motion of the system over time and how it is affected by the damping constant.

## 5. What are the units of the damping constant?

The units of the damping constant depend on the units of the other parameters in the formula being used. For example, in the formula for a damped harmonic oscillator, the units of the damping constant would be in force per velocity (N*s/m or kg/s).

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