2nd ordr homogenoues ODEs

the behavoiur of the solution of d^2x/dt^2+adx/dt+4x

depends on the value of a

Note a=alpha

a)find the ranges of a so that the solution displays

i)overdamping

ii)critical damping

iii)underdamping(decaying oscilations)

iv)growing oscilations

v)constant oscilations

b)For each of these cases, choose value of a within your stated

ranges, and find the general solution, displaying your solution

pictorially to show the behaviour of the solution

c) By carefully considering all the possible values of a identify the ranes which do not lead to the behavouirs listed in a, and describe the typical behaviour in this case

Re: 2nd ordr homogenoues ODEs

Quote:

Originally Posted by

**Magical** the behavoiur of the solution of d^2x/dt^2+adx/dt+4x

depends on the value of a

Note a=alpha

a)find the ranges of a so that the solution displays

i)overdamping

ii)critical damping

iii)underdamping(decaying oscilations)

iv)growing oscilations

v)constant oscilations

b)For each of these cases, choose value of a within your stated

ranges, and find the general solution, displaying your solution

pictorially to show the behaviour of the solution

c) By carefully considering all the possible values of a identify the ranes which do not lead to the behavouirs listed in a, and describe the typical behaviour in this case

You have not given an equation... I expect you meant $\displaystyle \displaystyle \begin{align*} \frac{d^2x}{dt^2} + \alpha\,\frac{dx}{dt} + 4x = 0 \end{align*}$.

Anyway, I suggest you read this article.

Re: 2nd ordr homogenoues ODEs

thanks, how do u write the eqaution like that, wihout useing / or a?

Re: 2nd ordr homogenoues ODEs

We use the inbuilt LaTeX compiler. You can go to the LaTeX sub forum for more information :)