second order ODE solution for this system??

karamustafa

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

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csprof2000

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)

Am I missing something, or does this answer your question?

karamustafa

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

csprof2000

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