Newtons 2nd Law corrected for Relativity

[SSGD]

F = d(mv)/dt Newtons 2nd Law
F = -kx Spring Force
F = -cv Damping Force

d(mv)/dt = -kx + -cv

How would you correct the equation for a damped harmonic oscillator for relativity. If it is possible. I just want a one dimensional solution unless you have to go to a two dimensional or three dimensional model to because of relativity.

 

[Meir Achuz]

$d(mv\gamma)/dt = -kx + -cv$, with $\gamma=1/\sqrt{1-v^2/c^2}.$

 

[SSGD]

That is it? You wouldn't have to correct x for length contraction or t for time dilation. Just correct the m as a function of velocity.

 

[Nugatory]

That is it? You wouldn't have to correct x for length contraction or t for time dilation. Just correct the m as a function of velocity.

That's right. They're your x and t coordinates, and you aren't moving relative to yourself.

 

[SSGD]

Oh... I understand. You have been a lot of help.

 

[SSGD]

From some of the reading I have done, magnetism is product of relativity and electric fields.

Columbic Force between a positive charge and a negative charge is

F = kpe/r² so because I am using my own position and time then check me if I have it.

d(mvγ)=kpe/r² or is there more to it because the two particle are moving relative to each other as well.

 

[Meir Achuz]

There is much more to it. The equation for the force between two moving charges needs special relativity if they have constant velocity, and 'retarded fields' if they are accelerating. This is covered in advanced EM texts.