Constant-Coefficient, Linear, Homogeneous 2nd-Order ODEs -- Transient & Steady-State Response
by Mike Martin

Consider a second-order, linear, constant-coefficent, homogeneous ordinary differential equation with sinusoidal forcing

a y " (t) + b y ' (t) + c y (t) = Fo sin (ω (t - δ))

with the initial conditions

y (0) = yo ,   y ' (0) = vo

Consider a response or solution on the interval from [0, tfinal]. For certain parameters values (a, b, & c all positive) & forcing functions, the signal response can be broken down into a transient response and a steady-state response. All three of these responses are plotted as functions of time, t. Note that the steady-state response often refers to what the second signal below becomes (or limits to) as the input, time, grows large.

Enter in the values of the parameters, then press the "Visualize" button.

a =

b =

c =


Fo =

ω =

δ =


yo =

vo =


tfinal =


ymin =

ymax =

y'min =

y'max =