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__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)?