# Math Help - resonance involing an ODE

1. ## resonance involing an ODE

Hi

my question is

For the ODE below, write down the forcing function $f(t)$that will lead to resonant behaviour $(t\rightarrow\infty)$. Verify your choice by calculating the particular intergral that corresponds to your forcing and examining its limit as $t\rightarrow\infty
$

a) $y^{(4)}+5\ddot{y}+4y=f(t)$

my solution to $y^{(4)}+5\ddot{y}+4y=0$ is $y_{c}=Asin(x)+Bcos(x)+Csin(2x)+Dcos(2x)$

thanks

2. Originally Posted by cooltowns
Hi

my question is

For the ODE below, write down the forcing function $f(t)$that will lead to resonant behaviour $(t\rightarrow\infty)$. Verify your choice by calculating the particular intergral that corresponds to your forcing and examining its limit as $t\rightarrow\infty
$

a) $y^{(4)}+5\ddot{y}+4y=f(t)$

my solution to $y^{(4)}+5\ddot{y}+4y=0$ is $y_{c}=Asin(x)+Bcos(x)+Csin(2x)+Dcos(2x)$

thanks
Ya - if you force your system with an $f(t)$ that contains any member of the complimentary solution it will resonant ${\it i.e.}$ if $f(t) = \sin t$ the solution will contain a terms like $t \sin t$ and $t \cos t$.