Driven Damped Harmonic Oscillator, f != ma?

  • #1
Driven Damped Harmonic Oscillator, f != ma??

Let's say I've got a driven damped harmonic oscillator described by the following equation:
[tex]A \ddot{x} + B \dot{x} + C x = D f(t)[/tex]

given that [tex] f = ma[/tex] why can't I write

[tex]A \ddot{x} + B \dot{x} + C x = D ma[/tex]

substitute [tex]\ddot{x} = a[/tex] to get

[tex]A \ddot{x} + B \dot{x} + C x = D m \ddot{x}[/tex]

and then rearrange to get

[tex](A - D m) \ddot{x} + B \dot{x} + C x = 0[/tex]

I know that's not how the problem is solved, but what is to stop me from solving it that way?
 
Last edited:

Answers and Replies

  • #2
90
0
Are you assuming constant acceleration?
 
  • #3
223
2
You're forgetting that f(t) is a time-varying force. You also have forces that depend on velocity and position, which is why what you wrote isn't correct. You only got the time-varying force.
 
  • #4
Meir Achuz
Science Advisor
Homework Helper
Gold Member
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Let's say I've got a driven damped harmonic oscillator described by the following equation:
[tex]A \ddot{x} + B \dot{x} + C x = D f(t)[/tex]

given that [tex] f = ma[/tex] why can't I write
The F in Newton 's F=ma is the net force, which does not equal the function f(t) in your problem.
 

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