Homework 6, due March 3, 1010

[goodwine]

Reading: Chapter 8.

Exercises: 8.12 - 8.18 from the course text.

[AL089]

For the last part of Problem 8.17, to find the transfer function from the input voltage to the angular velocity, can we simply multiply the the transfer function from voltage to angle by s? Since the angular velocity is just the first derivative of the angle, then the Laplace transform of that would be s*theta(s) wouldn't it?

[goodwine]

For the last part of Problem 8.17, to find the transfer function from the input voltage to the angular velocity, can we simply multiply the the transfer function from voltage to angle by s? Since the angular velocity is just the first derivative of the angle, then the Laplace transform of that would be s*theta(s) wouldn't it?

Exactly.

[mkiener]

Regarding finding the transfer function from the input to the output:

In class, we first took the Laplace transform of all the system equations, and then algebraically solved for the transfer function.

If it is possible to algebraically eliminate some variables before taking the Laplace transform (for example, for variables with no derivatives present), is that ok?

Thank you

[goodwine]

Regarding finding the transfer function from the input to the output:

In class, we first took the Laplace transform of all the system equations, and then algebraically solved for the transfer function.

If it is possible to algebraically eliminate some variables before taking the Laplace transform (for example, for variables with no derivatives present), is that ok?

Sure, it's exactly the same as eliminating them afterward. You can only algebraically eliminate variables before taking the Laplace transform if they always appear the same way, e.g., first derivative, of they only appear a few times so that you can differentiate one or more of the equations to get the term to appear the same way each time.

[Josh]

Professor,
For Problem 8.13 it says
f = t for t<t<1, cos(t-1) for 1<t.
Is this correct, or should it be
f = t for 0<t<1, cos(t-1) for 1<t

[goodwine]

Professor,
For Problem 8.13 it says
f = t for t<t<1, cos(t-1) for 1<t.
Is this correct, or should it be
f = t for 0<t<1, cos(t-1) for 1<t

You are right, it should be

t for 0<t<1

cos(t-1) for t>1