## Homework 6, due March 3, 1010

Due Wednesday, March 3, 2010.
goodwine
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### Homework 6, due March 3, 1010

Exercises: 8.12 - 8.18 from the course text.
Bill Goodwine, 376 Fitzpatrick
AL089

### Re: Homework 6, due March 3, 1010

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
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Joined: Tue Aug 24, 2004 4:54 pm
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### Re: Homework 6, due March 3, 1010

AL089 wrote: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.
Bill Goodwine, 376 Fitzpatrick
mkiener

### Re: Homework 6, due March 3, 1010

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
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Joined: Tue Aug 24, 2004 4:54 pm
Location: 376 Fitzpatrick
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### Re: Homework 6, due March 3, 1010

mkiener wrote: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.
Bill Goodwine, 376 Fitzpatrick
Josh

### Re: Homework 6, due March 3, 1010

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
Posts: 1596
Joined: Tue Aug 24, 2004 4:54 pm
Location: 376 Fitzpatrick
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### Re: Homework 6, due March 3, 1010

Josh wrote: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
Bill Goodwine, 376 Fitzpatrick