# ME 431 Homework

## Homework 01

On your marks... get set... Homework 01

Lyric of the day
You’ve got to trust your instinct,
And let go of regret.
You’ve got to bet on yourself now star,

For problem 5, my brain wants to believe that these springs are in series, but I’m having a hard time convincing myself and/or providing actual mathematical support. Any ideas?
Lots of ideas... how about this one: elements in parallel have the same displacement across each, but typically different forces; elements in series are subject to the same force, but with (possibly) different displacement. Here’s another one: derive the equations of motion for the system and identify the equivalent spring constant (whatever is in front of the displacement coordinate). Does it follow the rules for series (sum of the reciprocal constants) or parallel (sum of the constants)?
Right, so the idea of series is looking very good, as I can see that the rope would create a uniform force across both, but would create (possibly) different displacements. I think the main issue I’m having is defining coordinates that would link the displacements of both springs to that of the given x coordinate. I may be overthinking it.
To determine the overall displacement you have to use the equations of motion for the system. In this case it amounts to solving a static equilibrium problem.
I was overthinking it...

Hi. Could someone explain to me on problem #3 why the spring and damper forces all have the same sign, even though there is a spring and damper on each side of the block. When I did this problem and I summed the forces in the direction, I had the spring and damper forces acting to the left as negative and the right as positive. In the FBD on the solution, they all have a (-) sign. Thanks.
I think I know...

You have to be consistent between how you define the coordinates, and how the forces are related to those coordinates. In this problem x is measured positive to the right. So if the block moves to the right, the spring on the left extends, and the resulting force is to the left, so
F1 = -k1 x i

Also, for x > 0 (displaced to the right), the spring on the right compresses, and the resulting force is also to the left, so
F2 = -k2 x i

The same arguments hold for the dampers as well. Notice that I don’t pay any attention to which direction the arrows are pointing. I get all of my information from the definition of the force.