Driven Damped Harmonic Oscillator, f = ma?

[dimensionless]

Driven Damped Harmonic Oscillator, f != ma??

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

given that f = ma why can't I write

A \ddot{x} + B \dot{x} + C x = D ma

substitute \ddot{x} = a to get

A \ddot{x} + B \dot{x} + C x = D m \ddot{x}

and then rearrange to get

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

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

 

[desA]

Are you assuming constant acceleration?

 

[StatMechGuy]

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.

 

[Meir Achuz]

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

given that f = ma 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.