Mechanical math

This is a model with two degrees of freedom having two masses and two springs.

In the configuration shown aboveo the particles arc at their natural lengths.

The spring forces acting on the two particles are,

Hr: - k7.xe,i Hz: &n(x, -x7^)i H3:-H2--ku(xn-xii

Apply Newton's 2'd Law to,

particle A, ffi.a x.n= H1 + H2 : - k6xai + frs (rs - x7*) i.

particle B, ms )c.a = H3 : -lcy(xr-xa)I

Resolving in the I - direction and grouping the terms,

ffi.a fr.a= - (ko+ ks) xe + ks xs ke xA, ks xs

I txDH

I

i6l Particle A Particlc 8

ffinxg=

Pege 4