Bill Goodwine's Courses

Reading: Chapter 4

Exercises: 4.3, 4.4, 4.7, 4.9, 4.10, 4.12 and 4.27.

• For 4.3, only find the general solution. You do not need to find the constants c1 and c2 for the given initial conditions.
• For 4,7, also:
  • how does the solution change if m is slightly increased?
  • how does the solution change if k is slightly increased?
  • how does the solution change if b is slightly increased?

On Problem 4.3 are we supposed to do parts 1-4 or just find the general solution?

rlema wrote:On Problem 4.3 are we supposed to do parts 1-4 or just find the general solution?

You have to do 1-4. You can skip the part of part 1 that would make you find c1 and c2 based on the initial conditions.

On 4.4, are we asked to find an equation or plot an approximate steady-state solution?

rlema wrote:On 4.4, are we asked to find an equation or plot an approximate steady-state solution?

Equation. But I would note that you should be capable of plotting it too.

goodwine wrote:

rlema wrote:On 4.4, are we asked to find an equation or plot an approximate steady-state solution?

Equation. But I would note that you should be capable of plotting it too.

What exactly are we approximating based on the plots from 4.3 then?

rlema wrote:

goodwine wrote:

rlema wrote:On 4.4, are we asked to find an equation or plot an approximate steady-state solution?

Equation. But I would note that you should be capable of plotting it too.

What exactly are we approximating based on the plots from 4.3 then?

An equation that is the steady-state solution. It is only approximate because you can only determine values approximately from the figures.

For Problem 4.9, is there still a forcing function F(t) or is only gravity affecting affecting the system? And if F(t) is present, what function is it?

tduffy1 wrote:For Problem 4.9, is there still a forcing function F(t) or is only gravity affecting affecting the system? And if F(t) is present, what function is it?

There is still a forcing function, but just leave it unspecified as F(t).

For 4.10, can you post the Matlab codes used in class? I did not see them on this website.

mjunker1 wrote:For 4.10, can you post the Matlab codes used in class? I did not see them on this website.

They are only on the computer in the classroom, so I can do it tomorrow. There are examples in the book that are nearly exactly the same.

For 4.10 just to clarify, we are basically plotting the homogenous solution that we already found in question 4.3 for different zetas? Should we do all the work out again or can we just write out the equation of the homogenous solution from 4.3?

For problem 4.9, do we need to solve the differential equation of just leave it there? also does it have to be expressed in terms of omega and zeta? If we solve it, do we use variation of parameters?

nmejias wrote:For 4.10 just to clarify, we are basically plotting the homogenous solution that we already found in question 4.3 for different zetas? Should we do all the work out again or can we just write out the equation of the homogenous solution from 4.3?

You don't have to re-solve anything. In general if an answer is in the book or elsewhere in your homework, you can just refer to that. You could also use ode45().

rlema wrote:For problem 4.9, do we need to solve the differential equation of just leave it there? also does it have to be expressed in terms of omega and zeta? If we solve it, do we use variation of parameters?

You just need to determine the differential equation, not solve it. You don't have to do zeta and omega either. The point of the problem is the relationship between gravity and where x=0.

For 4.27 could you explain the motion of the problem? Is the mass rotating with the motor, or does the spring remain vertical the entire time?

dmontero wrote:For 4.27 could you explain the motion of the problem? Is the mass rotating with the motor, or does the spring remain vertical the entire time?

The eccentric mass, m_e, rotates around the shaft of the motor, which is sitting on top of the square mass. The square mass and spring are considered to only move up and down vertically.

For part 3 of problem 4.3, should we graph the plots in matlab, or is a rough sketch ok?

jmullen4 wrote:For part 3 of problem 4.3, should we graph the plots in matlab, or is a rough sketch ok?

All that is required is that you clearly communicate the nature of the solution.