Transfer function for a system with lossless gears

[theone]

Homework Statement

http://postimg.org/image/sd66qty27/

I am trying to understand the impedance terms for the equivalent system in (b)

Homework Equations

T1/T2 = N2/N1

The Attempt at a Solution

I just don't understand why the impedance before the gears have to be multiplied by (N2/N1)^2 before they can be added to the impedance after the gear.

 

[Subhash]

What is being done here, is that the load is being referred to the gear's output side. Let's say you had an object of moment of inertia L (load) being rotated through a lossless gear system of ratio N2/N1. If you apply Torque T as input, output torque is scaled by the gear ratio. Now if I ask you to choose a different load which behaves just the way this gear + load combination does, what would the moment of inertia of the simplified load be. Try to analyse what the T vs α would come out as in the case with gears and then try to get the same result out of a simple load without the gears. Follow the same approach for the given (albeit more complex) load in your problem statement.

 

[theone]

What is being done here, is that the load is being referred to the gear's output side. Let's say you had an object of moment of inertia L (load) being rotated through a lossless gear system of ratio N2/N1. If you apply Torque T as input, output torque is scaled by the gear ratio. Now if I ask you to choose a different load which behaves just the way this gear + load combination does, what would the moment of inertia of the simplified load be. Try to analyse what the T vs α would come out as in the case with gears and then try to get the same result out of a simple load without the gears. Follow the same approach for the given (albeit more complex) load in your problem statement.

Thanks very much!

I also have a couple of questions for (b) of the following question
http://postimg.org/image/uc0c581cb/
which has the solution
http://postimg.org/image/lr6hcp1ql/

1) why isn't an angle defined for the rotation of J2

2) for the fourth equation of motion (written for the second J=0), I can understand the theta 4 term but I don't understand the other term.