Hello I'm having a bit of trouble with analysing some of the coupled oscillator questions in terms of the energy functions.(adsbygoogle = window.adsbygoogle || []).push({});

Here is a coupled oscillator diagram:

http://img356.imageshack.us/img356/28/coupledlagr4fx.png [Broken]

Now for this one my main problem is that I don't know how to come up with the kinetic energy functions because there are the three masses there. By the way the question just asks you to find the lagrangian and hence find the equation of motion for the system.

What I know for this question is that it will obviously be moving about the point b/2 (the big block that is). I also don't really know how to find the moment of inertia for this object. I would have thought you would need the length of it, but it wasn't given in the question. And this is what I have for the kinetic energy function:

KE = (1/2)*I*[tex]\theta' ^2[/tex] + (1/2)m(x'+y')^2

Where x=2dsin[tex]\theta[/tex] and y = 2dcos[tex]\theta[/tex]

The reason I have 2 there is because I thought that's what you would do since both rods are displaced in the same direction and all.

For my potential energy function I have this:

potential is taken to be 0 at the black support

PE = -[tex]M_G[/tex]gdcos[tex]\theta[/tex] - 2mgdcos[tex]\theta[/tex]

From all this I can solve for the equation of motion, but I'm really not sure about it. I'd be grateful for any advice here.

Here is another diagram (not a coupled oscillator) that I'm having trouble with too.

http://img6.imageshack.us/img6/2290/secondlagra0tz.png [Broken]

In this case I really don't know how to do it. I know that it'd be rotational motion and all, but is the moment of inertia just the centre of mass moment of inertia plus md^2 where d = [sqrt([tex]a^2+b^2[/tex])]/2

This is what I have for the energies:

KE = (1/2)*I*[tex]\theta'^2[/tex]

PE = -[tex]M_c_m[/tex]gdcos[tex]\theta[/tex], where d is the distance of the centre of mass to the pivot point.

Again any help on either of these two questions would be great.

N.B. the prime (') means that it is the derivative with respect to time

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# Lagrangian Mechanics - coupled oscillator?

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