# Write different equation from physical system

• Maurizio
In summary, the conversation is about writing a differential equation to describe a system where force is the input and position is the output. The initial conditions are x1=0 and x2=0. The formula for the relationship between force and position for components such as spring and suspension are included in the attached file. The person is seeking suggestions on how to solve the problem and has found a result but is unsure if their starting equations are correct. They have provided their starting equations and the correct equations for comparison. They also mention making a mistake in their calculations.
Maurizio
Hi to all,

I've to write differential equation for desciribe system in attached file.

The system is intended: from force f as input to position x2 as output.

Initial condition are the following x1=0 and x2=0.

In the attached file I've included all formula for descrive relationship between force and position for components: Spring, suspension.

I'd like some suggestion about ho to resolve this kind of problem.

I've found result for this exercise, I've try to computate the valur, but I made samo mistake, cold you suggest if my starting equation are correct, if they're not could you explain my where I made error?

Starting Equation:
f + k(x1-x2) + BD(x1-x2)=D^2mx1
-k(x1-x2)-BD(x1-x2)=D^2mx2

Expand First and Second Equation
f +kx1 -kx2 +BDx1 -BDx2 = D^2mx1
-kx1 +kx2 -BDx1 +BDx2 = D^2mx2

Aggregate for common factor x1
( k + BD - D^2m )*x1 = -f + kx2 +BDx2
( -k -BD )*x1 = -kx2 -BDx2 +D^2mx2

Computate x1
x1 = ( -kx2 -BDx2 +D^2mx2 ) / ( -k -BD )

Replace x1 in first equation:
( k + BD - D^2m )*( -kx2 -BDx2 +D^2mx2 ) / ( -k -BD ) = -f + kx2 +BDx2

( k + BD - D^2m )*( -kx2 -BDx2 +D^2mx2 ) = (-f + kx2 +BDx2) * ( -k -BD )

-k^2x2 -kBDx2 + kD^2mx2 -BDkx2 -B^2D^2x2 +BD^3mx2 +kD^2mx2 + BD^3x2m D^4m^2x2
= +kf -fBD -k^2x2 -kBDx2 -kBDx2 -B^2D^2x2

+kD^2mx2 +BD^3mx2 +kD^2mx2 + BD^3x2m -D^4m^2x2
+kf -fBD

My result:
-D^4m^2x2 + BD^3x2m + BD^3mx2 +kD^2mx2 +kD^2mx2 = +kf -fBD

Correct Result:
+D^4m^2x2 + BD^3x2m + BD^3mx2 +kD^2mx2 +kD^2mx2 = +kf +fBD

Thank you very much!

Bye
Maurizio

#### Attachments

• system.JPG
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Last edited:
Maurizio said:
Replace x1 in first equation:
( k + BD - D^2m )*( -kx2 -BDx2 +D^2mx2 ) / ( -k -BD ) = -f + kx2 +BDx2

( k + BD - D^2m )*( -kx2 -BDx2 +D^2mx2 ) = (-f + kx2 +BDx2) * ( -k -BD )

-k^2x2 -kBDx2 + kD^2mx2 -BDkx2 -B^2D^2x2 +BD^3mx2 +kD^2mx2 + BD^3x2m D^4m^2x2
= +kf -fBD -k^2x2 -kBDx2 -kBDx2 -B^2D^2x2

Your mistake is in the multiplication (-f + kx2 +BDx2) * ( -k -BD ). On the right hand side rather than -fBD you should get +fBD

## 1. How do you write an equation for a physical system?

To write an equation for a physical system, you first need to identify the relevant variables and their relationships. Then, use mathematical symbols and operations to represent those relationships in equation form. It is important to ensure that the equation is consistent with the principles and laws governing the physical system.

## 2. What is the purpose of writing different equations for a physical system?

The purpose of writing different equations for a physical system is to accurately describe and predict the behavior and interactions of the system. Different equations may be needed to account for various factors and variables that affect the system, allowing for a more comprehensive understanding and analysis.

## 3. How does the form of the equation affect its interpretation?

The form of an equation can greatly impact its interpretation. For example, linear equations can provide information about the relationship between two variables, while differential equations can describe the rate of change of a variable over time. It is important to understand the form of an equation in order to properly interpret its meaning.

## 4. Can equations be used to model complex physical systems?

Yes, equations can be used to model complex physical systems. However, the accuracy of the model depends on the complexity of the system and the assumptions made in the equation. In some cases, simplifications may need to be made in order to create a manageable equation for analysis.

## 5. Are there specific rules for writing equations for physical systems?

There are general guidelines for writing equations for physical systems, such as using appropriate symbols and units, and ensuring the equation is consistent with the laws and principles governing the system. However, the specific rules may vary depending on the type of physical system being studied and the mathematical techniques used to represent it.

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