Understanding Spring-Coupled Masses: A Quick Guide

[*best&sweetest*]

[SOLVED] spring-coupled masses

Thanks, Doc Al... I think I understand it now!

 

[Doc Al]

Is it true that the potential energy U is just the sum of $$0.5kx_i^2$$ with $$i$$ going from zero to 4, or is it that $$U = 0.5 k x_1^2 + 0.5 k (x_2 - x_1)^2 + 0.5 k (x_3 - x_2)^2 + 0.5 k x_4^2?$$

What matters is how much each spring is stretched (or compressed). So the total spring potential energy is given by your second expression. (This is explained on the page that you linked.)

I'm equally confused with the kinetic energy...is it just
$$K = \Sigma (\frac{1}{2} mv_i^2)?$$

That's it.

 

[Shooting Star]

Thanks, Doc Al... I think I understand it now!

There's a first time for everything. That's a tautology almost. But this type of reply, by editing the very first post, is a first for me in the forum. The answer is left hanging with part of the query missing. I can't but help ask why?

 

[*best&sweetest*]

There's a first time for everything. That's a tautology almost. But this type of reply, by editing the very first post, is a first for me in the forum. The answer is left hanging with part of the query missing. I can't but help ask why?

If you are interested in the question, the entire question is quoted in Doc Al's post, and I managed to understand it by myself, so there is no need for other people to waste their time on it...that's why I deleted it.

 

[Shooting Star]

The more elegant way would be to mark the post as SOLVED.