The title of this page could be: Newton's Second Law Homework: Constant Term

[Niles]

Homework Statement

Hi

Say I am given Newtons second law in this form:

$$\frac{{d^2 x}}{{dt^2 }} + \gamma \frac{{dx}}{{dt}} + \omega _0^2 x + const = 0$$

I know the physical interpretation of all terms except the last one, i.e. the constant. Does this go into the restoring-force term, and hence create an un-symmetric potential?

 

[Apphysicist]

You might sometimes see it as mx''+bx'+kx=0, for a harmonic oscillator under friction. Since you have x''+nx'+w²x+C_=0, you again have a harmonic oscillator under friction (n=b/m, w²=k/m), but, as you might recognize if you moved C_ to the right-hand-side, you have an oscillator under forced resonance.

 

[ehild]

When C is a constant this is a damped oscillator that oscillates around x=-C/w instead of x=0. Like a mass hanging on a spring.

ehild