Is the D.E. Solution Affected by the Presence of a Non-Homogeneous Term?

[Darkmisc]

Homework Statement

Let ay'' + by' +cy = R(x)

Determining whether a system is under/over/critically damped depends on the size of b^2 compared to 4ac.

Does it depend at all on R(x)?

Homework Equations

Characteristic equation, quadratic equation.

The Attempt at a Solution

I've found a general solution to a D.E. where b^2 < 4ac, and is therefore underdamped (if the D.E = 0)

However, I'm not sure if I can still conclude that the system is underdamped if the D.E. = R(x).

 

[ehild]

Look after the definition of being under/over/critically damped.

ehild

 

[HallsofIvy]

Homework Statement

Let ay'' + by' +cy = R(x)

Determining whether a system is under/over/critically damped depends on the size of b^2 compared to 4ac.

Does it depend at all on R(x)?

No, it does not. As ehild suggests, surely the definition of "under/over/critically damped" is given in your text?

Homework Equations

Characteristic equation, quadratic equation.

The Attempt at a Solution

I've found a general solution to a D.E. where b^2 < 4ac, and is therefore underdamped (if the D.E = 0)

However, I'm not sure if I can still conclude that the system is underdamped if the D.E. = R(x).

 

[Darkmisc]

Thanks. The definition only referred to b^2 - 4ac without explicitly stating that R(x) was irrelevant to damping.

 

[ehild]

The term "damped" refers to the homogeneous equation. See this for example:

http://www.scar.utoronto.ca/~pat/fun/NEWT1D/PDF/OSCDAMP.PDF

ehild