Homework 6

[goodwine]

Reading: Chapter 4.

Exercises: 4.3, 4.4, 4.6, 4.7, 4.9, 4.12, 4.14 and 4.15.

In 4.6, you do not have to write a computer program, i.e., ignore the sentence starting with "Demonstrate whether..."

[ldillon1]

For 4.3, do we consider the force due to gravity as well?

[goodwine]

For 4.3, do we consider the force due to gravity as well?

No, see the note at the beginning of the exercises. Also problem 4.9 shows you don't have to ever consider it in these types of problems as long as you define x=0 in the right manner.

[bkenned7]

So, in 4.9, part 2 shows how defining equilibrium correctly allows you to ignore gravity, correct?
Can gravity be neglected in part 1 of 4.9 as well?

[kpulliam]

For question 4.9, what does it mean when it says "determine the equation of motion?" Does it want us to solve for x or just leave it as a diff eq?

[tbest]

Also for question 4.9, do we need to solve for the entire general solution, or can we concentrate on the steady state part of the equation?

[goodwine]

So, in 4.9, part 2 shows how defining equilibrium correctly allows you to ignore gravity, correct?
Can gravity be neglected in part 1 of 4.9 as well?

Yes to the first part, but no to the second because it's in comparing the two that allows you going forward to ignore gravity.

[goodwine]

For question 4.9, what does it mean when it says "determine the equation of motion?" Does it want us to solve for x or just leave it as a diff eq?

Find the differential equations. If it doesn't say to solve it, you don't have to solve it.

[goodwine]

Also for question 4.9, do we need to solve for the entire general solution, or can we concentrate on the steady state part of the equation?

You only need to find the equation, not solve it. But solving this specific equation should be easy anyway if you have already done so.

[goodwine]

Someone asked me:

For problem 4.3 on the latest homework, do you expect us to completely re-derive the answer to the equation in the method that you did in class, or do you expect us to be intuitively able to make changes to the solution that we found in order to reflect the different force acting upon the system? Or should we solve it without converting to the constants that we have been using lately in class?

Completely re-derive it mathematically. There are enough steps in there that people find confusing, that you need to go through it all. You also do need to convert the to the constants because it asks you to plot the magnitude and phase vs frequency ratio, and it's not possible to do that without that conversion.

[goodwine]

Someone asked me:

I'm a bit confused about the wording of some of the questions for Problem Set 6. Does "Determine a good approximation" mean write out an equation for M similar to what we did in part 3 of problem 4.3, or does it mean draw a graph approximating the value of M for different omega values, or both of these things? (This is particularly a question for Problems 4.4 and 4.7).

Neither. It means use the graphs to determine an answer like x = 13 cos(5 t + 2) where the numbers came from the graphs (that's the only approximate part, you can't find exact values from graphs).

[colsen3]

Does steady state imply that w=wn?

[goodwine]

Does steady state imply that w=wn?

No, it implies that time is large. If there is damping the homogeneous solution will be close to zero.

[colsen3]

Also, is displacement transmissibility the same as force transmissibilty?

[colsen3]

Does steady state imply that w=wn?

No, it implies that time is large. If there is damping the homogeneous solution will be close to zero.

But in problem 4.12 I think we are supposed to substitute using wn=sqrt(k/m) to solve for k to manipulate the equation . But we originally have w and not wn.

[goodwine]

Does steady state imply that w=wn?

No, it implies that time is large. If there is damping the homogeneous solution will be close to zero.

But in problem 4.12 I think we are supposed to substitute using wn=sqrt(k/m) to solve for k to manipulate the equation . But we originally have w and not wn.

There are lots of wn's inside M_f.

[Jfox10]

For problem 4.15, do we need to assume initial conditions in order to eliminate the c1 and c2 that are found when calculating position function (as part of getting to the energy function), or do they end up playing an insignificant role?

[goodwine]

For problem 4.15, do we need to assume initial conditions in order to eliminate the c1 and c2 that are found when calculating position function (as part of getting to the energy function), or do they end up playing an insignificant role?

Yes, but I would suggest choosing the initial conditions such that c1 and c2 are both zero.