Morin classical mechanics differential equation problem

In summary: Interesting @malawi_glenn ! Well, I got an offer to skip to second year university physics next year in NZ if I don't want to go for my finial year of high school (year 13 is what they call it over here). So, I've just been preparing a bit for that. Reading morins for it is probably over preparing for it thought!
  • #1
ChiralSuperfields
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Homework Statement
Please see below
Relevant Equations
d^2x/dt^2 = dv/dt = a
I was reading the oscillations chapter which was talking about how to solve linear differential equations. He was talking about how to solve the second order differential below, where a is a constant:
1670386433801.png

In the textbook, he solved it using the method of substitution i.e guessing the solution. However, how would we solve this differential equation using the method of separation of variables?

I tried solving it using the definition of acceleration, however, I don't think you can do that since v is the derivative of x.
1670386779900.png

However, if we do use definition of the position,
1670387157698.png


Many thanks!
 
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  • #2
You wouldn’t. It is not an ODE of the form ##x’ = f(x) g(t)##.

The typical way of solving a linear ODE with fixed coefficients is to make the ansatz ##e^{kt}## and find the allowed values of k.
 
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  • #3
Orodruin said:
You wouldn’t. It is not an ODE of the form ##x’ = f(x) g(t)##.

The typical way of solving a linear ODE with fixed coefficients is to make the ansatz ##e^{kt}## and find the allowed values of k.
Thank you @Orodruin !
 
  • #4
Aren't differential equations of the form ##y'' = ky## a prerequisite for classical mechanics classes these days?
 
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  • #5
malawi_glenn said:
Aren't differential equations of the form ##y'' = ky## a prerequisite for classical mechanics classes these days?
@malawi_glenn I'm a not taking any classical mechanics classes. I'm a year 12 from New Zealand (Still got a year of high school to go).
 
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  • #6
malawi_glenn said:
Aren't differential equations of the form ##y'' = ky## a prerequisite for classical mechanics classes these days?
Not necessarily. Even back in the old days when I took classical mechanics, I saw how to solve ##y''-2by'+\omega^2y=0## in classical mechanics taught by the physics department before I saw it in an ODE course taught by the math department. If you think about it, classical mechanics is, in most places, a fourth semester course after three semesters of intro mechanics, E&M and 20th century physics a.k.a. Modern Physics. Concurrent with these are three semesters of calculus. By the time students are ready to take classical mechanics, an ODE course would at best be a co-requisite, not a prerequisite.
 
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  • #7
kuruman said:
Not necessarily. Even back in the old days when I took classical mechanics, I saw how to solve ##y''-2by'+\omega^2y=0## in classical mechanics taught by the physics department before I saw it in an ODE course taught by the math department. If you think about it, classical mechanics is, in most places, a fourth semester course after three semesters of intro mechanics, E&M and 20th century physics a.k.a. Modern Physics. Concurrent with these are three semesters of calculus. By the time students are ready to take classical mechanics, an ODE course would best be a co-requisite, not a prerequisite.
Thank you @kuruman for the info! To be a physics major in NZ you don't even have to take an ODE course as a requirement, which is kind of surprising compared to what they make US physics majors take.
 
  • #8
Callumnc1 said:
@malawi_glenn I'm a not taking any classical mechanics classes. I'm a year 12 from New Zealand (Still got a year of high school to go).
We do basic ODE's in swedish high school, year 12.
Just doing morin for fun?
 
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  • #9
malawi_glenn said:
We do basic ODE's in swedish high school, year 12.
Just doing morin for fun?
Interesting @malawi_glenn ! Well, I got an offer to skip to second year university physics next year in NZ if I don't want to go for my finial year of high school (year 13 is what they call it over here). So, I've just being preparing a bit for that. Reading morins for it is probably over preparing for it thought!

Many thanks,
Callum
 

1. What is the Morin classical mechanics differential equation problem?

The Morin classical mechanics differential equation problem is a mathematical problem that involves solving a system of differential equations in classical mechanics. It is commonly used to model the motion of objects under the influence of forces, such as gravity or friction.

2. Why is the Morin classical mechanics differential equation problem important?

The Morin classical mechanics differential equation problem is important because it allows scientists and engineers to accurately predict the motion of objects in real-world scenarios. This is essential for developing technologies and understanding natural phenomena.

3. What are some common applications of the Morin classical mechanics differential equation problem?

The Morin classical mechanics differential equation problem is used in a variety of fields, including physics, engineering, and astronomy. Some common applications include predicting the trajectory of projectiles, analyzing the motion of celestial bodies, and designing structures to withstand external forces.

4. What are some techniques for solving the Morin classical mechanics differential equation problem?

There are several techniques for solving the Morin classical mechanics differential equation problem, including separation of variables, variation of parameters, and Laplace transforms. Each technique has its own advantages and may be more suitable for different types of problems.

5. Are there any limitations to the Morin classical mechanics differential equation problem?

While the Morin classical mechanics differential equation problem is a powerful tool for predicting motion, it does have some limitations. It assumes that the system being studied is in a state of equilibrium and does not take into account factors such as air resistance or non-conservative forces. Additionally, it may not accurately model systems with complex or chaotic behavior.

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