# Second order ODE into a system of first order ODEs

## Homework Statement

The harmonic oscillator's equation of motion is:

x'' + 2βx' + ω02x = f

with the forcing of the form f(t) = f0sin(ωt)

## The Attempt at a Solution

So I got:
X1 = x
X1' = x' = X2
X2 = x'
X2' = x''
∴ X2' = -2βX2 - ω02X1 + sin(ωt)

The function f(t) is making me doubt this answer because I have to take into account f0 and it just disappears in the solution.

(For context I have to put it into a system of first order ODEs because I have to code it into python and plot the results with the given parameters.)

Am I on the right track? Or am I missing anything?

## Answers and Replies

Related Calculus and Beyond Homework Help News on Phys.org
BvU
Homework Helper
2019 Award
it just disappears in the solution
Looks to me you made it disappear in the equations already.

Looks to me you made it disappear in the equations already.
Oh so I shouldn't have taken it out in the first place then? That makes sense thanks! Other than that, am I missing anything else?

BvU