- #1

caius

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## Homework Statement

I have a problem where I have a mass suspended in a system of springs. I need to differentiate the equation wrt time so I can can show equivalence with Newton's second law.

The mass and springs are vertically aligned so the motion is in one dimension. The actual problem has several springs, but for simplicity I am describing a system with just two. The equation below I think shows the total energy of the system.

## Homework Equations

E = 1/2 mv^2 + k(x-l)^2 + 2k(l-x)^2 -mgx

where m=mass, v= velocity, k= stiffness, x=current position and l=spring's natural length.

## The Attempt at a Solution

I think the way to approach it is to substitute dx/dt in place of the velocity, however I can't see what to do with the spring parts.

I seem to have some kind of mental block on this, and it's very frustrating. Any assistance on how to approach it would be gratefully received!