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October 9th, 2012, 08:01 AM   #1
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Differential Equation

For the following problem it is given: Summation of F = 0 Write a differential equation for this mechanical system. Put it in the form dx/dt + P(t)X = Q(t)

Given Info: 1st order Linear Ordinary Differential Equation (linear ODE) = dx/dt + P(t)X=Q(t)

2nd order Linear ODE = (d^(2)x)/dt^(2) + P(t)dx/dt + Q(t)X = R(t)

Mass in this system is zero (i.e. there is no mass)

Use Newton's Second Law of Motion to write an equation and solve for X. (Newton's 2nd Law of Motion for this particular problem is Summation of all F = 0)

Thus we get Fsub 1 - Fsub k = 0 so then Fsub1 - KX = 0 so then Fsub1 = KX so then X = Fsub1/K

Note: This is not a differential equation, it is an algebraic equation.

The first problem we have a damper only (AKA a "dashpot")

Fsub1 = Applied Force (To be determined in another project later in this course)
X = Amount the damper is compressed
Fsub b = b dx/dt = force produced by the damper action when it is compressed (b is a constant also to be determined later in this course NOT NOW!)

Again, the MASS in this system is zero. Newton's second law of motion for this problem/system is Summation of F = 0

(One of the fundamental laws used in mechanical engineering is Newton's second law of motion. It is used extensively in mechanical engineering. Summation of F = ma, where a = (d^(2)x) /(dt^(2)

Given Info:

K=spring constant Fsubk = KX = force produced by spring when it is compressed by a distance of X.
X=amount the spring is compressed by Fsub1
Fsub1 = applied force
For this project we will say that upward forces are negative; Downward forces are positive. There are only 2 forces for this problem

Question #1: Using Summation of F = 0, write a differential equation for this mechanical system. Put it in the form dx/dt+P(t)X=Q(t)

As a new calculus student I have been given this 14page handout and it was not covered in class. I have read over it many times and am not at
that I can comprehend what it is saying. Frustration can be so toxic to a new math student and I see it in others in math classes at times
too. I pray someone on the site can walk me through this and explain to me what it is wanting me to do. Please do not reply to this forum or
post in a way that will confuse me more than I already am.

Thanks a million for any and all help on the project!

mathkid is offline  

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