Thread: 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

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 .

Anyway, I suggest you read this article.

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

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