# Newtons 2nd Law corrected for Relativity

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

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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
Mentor
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.

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

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