[saved-setup]
[labels]
title=Second Order Differential Equations for Simple Harmonic Motion
xaxis=x
yaxis=y

[grid]
left=-7
right=7
top=auto
bottom=auto

[options]
detail=dots
axes=1808
labels=on

[equations]
d2x + 2dx + x = 0 {0,1,0}  ' critically damped
dx + y = 0 ; dy = x {0,1, 1}  ' perfect SHM using ODE system (dx = d^2y/dt^2)
d2x + 1/2dx + x = 0 {0,1,0} ' underdamped
d2x + x = 0 {0,1,0} ' perfect simple harmonic motion
d2x + 3dx + x = 0 {0,1,0} ' overdamped