# ME 431 Homework

## Spring 2018, Homework 03

It’s time... for Homework 03

What is meant by “Rewrite the (second-order) equation of motion as a pair of first-order differential equations.”? I’m not sure what is being asked.
If you identify the velocity as
v = dx/dt
then the acceleration can be written as
a = dv/dt
Therefore the equation of motion can be written as an equation for dv/dt, together with the definition of the velocity above.

For question one part two regarding the stability of the equation of motion, just to be clear, you are looking for a range or set of values correct?

I’m having a hard time figuring out what the moment of inertia is for objects. Specifically for problem 1. All I can find for bars is ml^2/12.
I use the equation I_o = I_g + md
2
This I believe the the parallel axis theorem. So (ml
2)/12 is the I_g. d the distance your are moving the axis of rotation.
In general, if the inertia of an object about its mass center
is known (IG), the inertia about any other point may be calculated with
the parallel-axis theorem as
IP = IG +md*d (d squared. The carrot up symbol does something to the post),
where d is the distance between G and P.

IG=(mL*L)/12 (Inertia about the mass center)

If the bar is fixed on the end, you are looking for the inertia from the end of the bar (IA)
IA=(mL*L)/3

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