The Student Room Group
Competition - post a photo you've taken of nature >>
Competition - post a photo you've taken of nature >>
Competition - post a photo you've taken of nature >>

Non homogeneous second order ODE

d2xdt2+kdxdt+x=cos⁡Ωt\frac{d^{2}x}{dt^{2}}+k\frac{dx}{dt}+x=\cos\Omega t

Where Ω\Omega is a positive constant and the constant kk lies in the interval 1≤k<21\leq k < 2

I'm familiar with solving second order ODEs however the constant k lying in that interval is throwing me off. Could someone walk me though it?
Original post by nugiboy
d2xdt2+kdxdt+x=cos⁡Ωt\frac{d^{2}x}{dt^{2}}+k\frac{dx}{dt}+x=\cos\Omega t

Where Ω\Omega is a positive constant and the constant kk lies in the interval 1≤k<21\leq k < 2

I'm familiar with solving second order ODEs however the constant k lying in that interval is throwing me off. Could someone walk me though it?

It would probably be more helpful if you posted your attempt at it and hopefully I, or someone else, will be able to get you back on the right track.
Reply 2
Avatar for ztibor
ztibor
10
Original post by nugiboy
d2xdt2+kdxdt+x=cos⁡Ωt\frac{d^{2}x}{dt^{2}}+k\frac{dx}{dt}+x=\cos\Omega t

Where Ω\Omega is a positive constant and the constant kk lies in the interval 1≤k<21\leq k < 2

I'm familiar with solving second order ODEs however the constant k lying in that interval is throwing me off. Could someone walk me though it?


The interval of k only means that the caharacteristic polynomial of homogeneous part will have complex roots. Solve according to this.

Quick Reply

Related discussions

Latest

Trending

Trending

Articles for you