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# Mechanics, Potential Energy of a Spring (Lagrangian Mechanics) watch

1. I'm trying to solve this question but I'm failing at the first step.

I'm supposed to get the Kinetic Energy into the form and the Potential energy into the form where M and K are dxd matrices.

I can do it for the k.e. but not for the p.e. as I don't know how to work out the p.e. of a spring. My notes say "The potential energy of each spring is k/2 times the square of the displacement from the natural length." - I don't know what that means.

Could someone show me how to work out the p.e.
2. (Original post by primaverasnap)

I'm trying to solve this question but I'm failing at the first step.

I'm supposed to get the Kinetic Energy into the form and the Potential energy into the form where M and K are dxd matrices.

I can do it for the k.e. but not for the p.e. as I don't know how to work out the p.e. of a spring. My notes say "The potential energy of each spring is k/2 times the square of the displacement from the natural length." - I don't know what that means.

Could someone show me how to work out the p.e.
Well, you know hooke's law right?:

integrating both sides w.r.t x gives us the work done i.e the potential energy in the spring:
3. So would the p.e. = k/2 (q1^2 + (q2 - q1)^2 + (3a - q2)^2) ?

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Updated: November 27, 2011
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