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Normal Modes - One Dimensional Oscillating Systems

  • Thread starter moolimanj
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Hi

Can someone help me with the following questions please (see attachment)?

I really need some help on the following:

i). Drawing a force diagram for each particle (I really hate drawing these).

As a guess for m1, am I right in thinking that H and N point up and W points down? But do I also need to add m3 to W (or would it be half m3?)

And for m3, would it be H1 and H2 up together with N, and W pointing downwards? Or would I also need to include m1 and m2?

ii). Can someone help me indicate the changes in forces exerted by the springs when the particles are displaced from their equilibrium positions? (the forces need to be expressed as vectors in terms of stiffness and displacements.)

iii) How do I derive the equation of motion of each particle?
 

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