# Second order ODE solution for this system?

## Main Question or Discussion Point

second order ODE solution for this system??

hello guys,
I am wondering if what is the analytical solution for this system?
can we solve it as a mass-spring-damper system?
the rectangular part is removed from the disk.

[URL=http://img3.imageshack.us/my.php?image=odev.jpg][PLAIN]http://img3.imageshack.us/img3/3610/odev.th.jpg[/URL][/PLAIN]

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So the DE is

ax'' + bx' + cx = 0

Write the characteristic equation...

an^2 + bn + c = 0

Solve for n using the quadratic formula...

n = [-b +- sqrt(b^2 - 4ac)] / 2a

This will give you two (possibly non-unique) exponents. if the exponents are different, say n1 and n2, then the solution is

x(t) = Aexp(n1 t) + Bexp(n2 t)

If the exponents are the same, then

x(t) = Aexp(n t) + B t exp(n t)

thanks a lot, that is the answer if the motion is linear, how about the angular motion?
how can i modify this equation.??

To make it angular, rewrite it using "theta" instead of "x".