Homework 7, due October 13.

[goodwine]

Reading: By now you should have read all of chapters 1 - 4 except section 1.6 from Chapter 1.

Exercises: 4.17, 4.19, 4.26 and 4.27.

For 4.26, x in the equation is the displacement of the end of the beam in the downward direction. It is NOT along the axis of the beam, as the figure indicates.

[bkenned7]

4.27 Part 3
How do we plot |x_p/r| ? The x_p that I calculated has multiple unknowns in it (mass and k). Guessing this is wrong?
Since it says to compare to Figure 4.5, is eccentricity equal to the magnification factor?

[goodwine]

4.27 Part 3
How do we plot |x_p/r| ? The x_p that I calculated has multiple unknowns in it (mass and k). Guessing this is wrong?
Since it says to compare to Figure 4.5, is eccentricity equal to the magnification factor?

Get it in terms of frequency ratio and then you should be able to plot it vs frequency ratio for various damping ratios, i.e., get it like the other magnification factor plots.

[jmcgill1]

4.27

Is there a damper in this problem or not? The problem statement says the motor is attached to a mass-spring-damper system, but Fig 4.33 doesn't seem to have a damper attached. Also were supposed to compare our plot to Figure 4.5, which corresponds to modeling systems with forced, undamped vibrations.

[goodwine]

4.27

Is there a damper in this problem or not? The problem statement says the motor is attached to a mass-spring-damper system, but Fig 4.33 doesn't seem to have a damper attached. Also were supposed to compare our plot to Figure 4.5, which corresponds to modeling systems with forced, undamped vibrations.

No damper in the picture, so you can assume no damping. Yes, if your plot is any different, explain why and connect the answer to the physics of the problem.

[ekearney]

Are we to assume that the mass me and mass m are the same so that they cancel each other out for the steady-state ratio solution?

[goodwine]

Are we to assume that the mass me and mass m are the same so that they cancel each other out for the steady-state ratio solution?

No (and that should make some sense if you think what this problem is modeling).

[mrosset1]

For 4.26 do we take into account the force gravity has on the mass?

[goodwine]

For 4.26 do we take into account the force gravity has on the mass?

No, the point of the gravity problem in the last homework is that there is no need to do so.

[kpulliam]

For Problem 4.27 in part 3 it tells us to plot |xp/r| versus w/wn is the r in the |xp/r| the fixed distance or the ratio w/wn?

[goodwine]

For Problem 4.27 in part 3 it tells us to plot |xp/r| versus w/wn is the r in the |xp/r| the fixed distance or the ratio w/wn?

It's the fixed distance of the eccentricity. I'm going to send an email to the whole class shortly on that problem.

[goodwine]

Someone asked me:

I have a question about problem 4.27 part 1. I think I told you that I am using my roommate's book. In his book, he changed the forcing function we are supposed to prove to have a sine instead of a cosine. Do I ignore that change? I would assume so, but I want to make sure.

You can use sine or cosine, it really doesn't matter.