Following to article of “A Model to
Solve a System of Nonlinear Equations by Using Microsoft Excel plus VBA” (http://emfps.blogspot.com/2018/02/a-model-to-track-location-of-particle.html), the purpose of this article is,
to present another example about solving a system of nonlinear equations for
Simple Harmonic Motion (SHM).
Suppose
we have two oscillatory motions which are in two perpendicular directions. We
can write a system of equations for them as follows:
Assume the angular frequency for both SHMs is the same and
also there is the difference between initial phases equal 90 degree. In this
case, we will have below system of equations:
This model is able to solve above
system of two equations for given data of “x”, “y”, “Ax” and “Ay”.
Method (1):
The convert of two equations to one equation
and solving only one equation for three independent variables in accordance
with the method mentioned in article of “Solving
a Nonlinear Equation with Many Independent Variables by Using Microsoft Excel
plus VBA” (https://emfps.blogspot.com/2016/10/can-we-solve-nonlinear-equation-with.html) as follows:
Below figure as well as shows you
the components of this model:
Let me explain you about the
components of above model as follows:
1. In right side on cells L6:O6, we
have inputs including given data of
“x”, “y”, “Ax” and “Ay”.
2. In left side on cells H6:J7, we
have other inputs including lower and upper ranges for independent variables of
“ω”, “t” and “φ” to reach the answers which are the solution for system of two nonlinear equations. Here, there are lower and upper
ranges which are changed by click on cell A2 and also this change will again go
back by click on cell B2 (Go & Back).
3. On cells H10:J24,
we have outputs which are the answers to above system
of two nonlinear equations.
4. On cell M7, we have Error which
is the difference between equation of outputs (-y.Ax /x.Ay) and equation of
inputs (Tan (ωt+φ))
5. On cells K10:K24, we have the
solution of “x” by replacing the answers.
6. On cells M10:M24, we have the
solution of “y” by replacing the answers.
7. On cells O10:O24, we have the
difference between item 5 (“x”) and cell L6 which are the errors of our answers.
8. On cells P10:P24, we have the
difference between item 6 (“y”) and cell M6 which are the errors of our answers.
You can see below clip as the
examples for this model:
Method (2):
Using the method stated in article
of “A Model to Solve a System of Nonlinear Equations by Using Microsoft Excel
plus VBA” (http://emfps.blogspot.com/2018/02/a-model-to-track-location-of-particle.html
In this method, we directly solve a system of two nonlinear
equations.
Below figure as well as shows you
the components of this model:
The explanations of the components
are the same with method (1) except the error.
You can see below clip as the
examples for this model:
All researchers and individual people, who are interested in having
this model, don’t hesitate to send
their request to below addresses:
