Finding solutions to equations of motion

In summary, the problem at hand involves finding the solution for x, where x'' +2yx' +w^2 =fe^t, for a critically damped oscillator with a natural frequency (w) equal to the coefficient of friction (y). The proposed solution is Afe^t where A=f/4, but there seems to be a discrepancy in the use of "f" as it is also used as a variable in the equation f=mfe^-t. Clarification on the meaning of "f" and the dimensions of the solution are needed for further progress.
  • #1
Ed Quanta
297
0
Ok, so I am dealing with a critically damped oscillator in which the natural frequency(w) of the oscillator is equal to the coefficient of friction (y). I am given the force mfe^t and told to find a solution for x, where

x'' +2yx' +w^2 =fe^t.

How do I go about doing this? The solution that I am supposed to find is Afe^t where A=f/4

I have to solve this for f=mfe^-t also, if this requires a different strategy, let me know I guess.
 
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  • #2
It would help a lot if you would clarify what you are saying. There is clearly a typo in your equation: it should be
x'' +2yx' +w^2x =fe^t.

But the main problem is that you seem to be using "f" to mean at least two different things. You say "I am supposed to find is Afe^t where A=f/4". Is that f<sup>2</sup>e<sup>t</sup>? But then "I have to solve this for f=mfe^-t". Surely f doesn't mean the same thing on both sides of that equation (since me<sup>-t</sup> is not 0!).
 
  • #3
I doubt whether the Pro is correct

And what are the dimensions on both sides of the solution
 
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1. What is an equation of motion?

An equation of motion is a mathematical representation of the relationship between an object's position, velocity, and acceleration over time. It is often used in physics and engineering to describe the motion of objects.

2. How do you solve equations of motion?

To solve an equation of motion, you need to have information about the initial conditions of the object's motion, such as its initial position, velocity, and acceleration. You can then use mathematical methods, such as calculus, to manipulate the equation and solve for the unknown variables.

3. What are the types of equations of motion?

There are three main types of equations of motion: constant acceleration equations, uniformly accelerated motion equations, and equations for projectile motion. Each type is used to describe different types of motion and requires different initial conditions and mathematical methods to solve.

4. Why are equations of motion important?

Equations of motion are important because they allow us to mathematically model and predict the motion of objects. This is crucial in many fields, such as physics, engineering, and astronomy, where understanding and predicting the behavior of moving objects is essential.

5. Can equations of motion be used in real-world situations?

Yes, equations of motion are often used in real-world situations to solve problems and make predictions. For example, they can be used to calculate the trajectory of a projectile, the motion of a falling object, or the acceleration of a car. They are also used in designing and testing structures, such as bridges and buildings, to ensure their stability under different forces and motions.

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