# Dashpot Equation For Voigt

• yosimba2000
In summary, the proposed way to find the Voigt model is incorrect because n(dx/dt) is not included in the equation and kx + nx/t cannot be solved for without it.
yosimba2000
Problem:
So I already know how to correctly find the formula for a Voigt model, but why is my proposed way incorrect?

Equations and Assumptions:
for dashpot: F = n(dx/dt), where n is the dashpot constant and dxdt is change in distance/change in time
for spring: F = kx

assuming: arm connecting dashpot and spring doesn't bend or rotate, then F applied is equal to Force on Spring + Force on Dashpot. Also, because the arm doesn't bend, displacement of Dashpot and Spring are equal.

the correct equation: X = F(1-exp(-kt/n))

My Proposed Method:
Force on spring + Force on dashpot = total Force (A)
F + F = F
kx + n(dx/dt) = F

n(dx/dt) is Force on dashpot.
why can't I separate to get: (ndx) = (Force on dashpot)dt
then integrate to get, both from 0 to respective final values, to get (nx) = (Force on dashpot)(t)
Then solve for Force on dashpot to get nx/t
Then plug this in for Force on dashpot in equation (A)
kx +nx/t = total Force
Solve for X
X = (F)/[(k+n)/t]

Essentially, what I am asking is: why do I HAVE to leave the dx/dt in the dashpot equation as is? Why can I not just say F = n(dx/dt), then separate and integrate to get F = nx/t, and then just substitue this in equation (A)?

yosimba2000 said:
Force on spring + Force on dashpot = total Force (A)
F + F = F
kx + n(dx/dt) = F

n(dx/dt) is Force on dashpot.
why can't I separate to get: (ndx) = (Force on dashpot)dt
Because it isn't. How do you justify ignoring kx there?

I'm no maths expert, but it does seem like it must be:

kx. dt + n. dx = F. dt

I'm assuming that the dashpot and spring are arranged so that their forces are summed, but not necessarily equal?

Anyway, I've given you something to mull over while we wait for an expert to stroll by. :)

This is not a physics question. This is a math question on how to solve first order linear ordinary differential equations. You need to go back to your math book and review.

## 1. What is the Dashpot Equation for Voigt?

The Dashpot Equation for Voigt is a mathematical model used to describe the behavior of a viscoelastic material. It combines elements of both the spring and dashpot models to better represent the viscoelastic properties of certain materials.

## 2. How is the Dashpot Equation for Voigt derived?

The Dashpot Equation for Voigt is derived using the principles of linear viscoelasticity. It combines Hooke's Law, which describes the relationship between stress and strain in a spring, with Newton's Law of Viscosity, which describes the relationship between stress and strain rate in a dashpot.

## 3. What are the parameters in the Dashpot Equation for Voigt?

The parameters in the Dashpot Equation for Voigt are the spring constant (k) and the dashpot coefficient (η). These parameters represent the stiffness of the material and its resistance to deformation, respectively.

## 4. What is the significance of the Dashpot Equation for Voigt?

The Dashpot Equation for Voigt is significant because it is able to accurately model the behavior of viscoelastic materials, which have both elastic and viscous properties. This equation is particularly useful in the study of materials such as polymers and biological tissues.

## 5. How is the Dashpot Equation for Voigt used in practical applications?

The Dashpot Equation for Voigt is used in practical applications in various fields such as engineering, biomechanics, and materials science. It helps to predict the behavior of viscoelastic materials under different loading conditions, which is essential in designing structures and products that can withstand repeated stresses and strains.

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