ME 431 Homework

posts: 5
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.
posts: 9
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.

posts: 3
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?

posts: 2
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.
posts: 5
I use the equation I_o = I_g + md
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.
posts: 1
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)