1. ## ODE Problem

Is anyone able to do this?
Im having lots of problems

2. ## Re: ODE Problem

For $\displaystyle \displaystyle \frac{d^2i}{dt^2}+400i= 0$ what is the charactersitic equation? You will need to solve this equation to contiune.

3. ## Re: ODE Problem

There's probably an easier way to do this, but one valid and straightforward method is to convert to the system

$\displaystyle \left[\begin{array}{c}x_1\\x_2\end{array}\right]'=\left[\begin{array}{cc}0&1\\-400&0\end{array}\right]\left[\begin{array}{c}x_1\\x_2\end{array}\right]$,

where $\displaystyle i(t)=x_1$. We use this to find the fundamental matrix

$\displaystyle X(t)=\left[\begin{array}{cc}-\cos 20t&(\sin 20t)/20\\20i\cos 20t&i\sin 20t\end{array}\right]$

and determine $\displaystyle i(t)=a(-\cos 20t)+b(\sin 20t)/20$ for some constants $\displaystyle a,b\in\mathbb{R}$. It's easy to verify that the solution to the IVP in (i) is then given by $\displaystyle i(t)=5\cos 20t$.

4. ## Re: ODE Problem

I should have been more specific sorry. its part ii) that Im really stuck with. sorry
for part i) I put the values into the quadratic formula and then with the obtained values substituted them into general solution giving me the desired graph that i was looking for
If you could help me with part ii) that would be great.
thanks

5. ## Re: ODE Problem

Originally Posted by Bullet