# Thread: 2nd ordr homogenoues ODEs

1. ## 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

2. ## Re: 2nd ordr homogenoues ODEs

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*}.