# Thread: System Modeling and integration problem. Need help?

1. ## Distance between the plates: Integration problem

There are two plates, green and blue as shown in the diagram below.

The green plate can move, due to which the distance R between the plates changes.

R at a height of h will be

R=(H d2+∆d1 h)/H

What will be the equation for integral of R for complete height H. Please explain the solution. I tried to solve it but came up with log(H)-log(0) in the equation. Log 0 cannot be solved.

Thankyou for your help

2. Hi

Not sure to have well understood your question
Anyway ...
If you want to calculate the mean distance between the two plates

$\frac1H\int_{0}^{H}\left(d_2+\frac{\Delta d_1}{H}\:h\right)dh=d_2+\frac{\Delta d_1}{2}$

But this can be found geometrically without using integrals