How many different velocities for this rotational mechanical system?

[dla]

Homework Statement

I need to write the equations of motion for the mechanical system below. So I need to know how many velocities there are in the system, the answer key says there's only 4 but shouldn't there be 5? I am unsure if the J3 mass has it's own velocity from the point between K_2 and the combination of D_2 and K_3.

Homework Equations

The Attempt at a Solution

I have marked the places I believed there is a different velocity in blue. Any help would be very much appreciated.

Homework Statement

 

[Simon Bridge]

Welcome to PF;
I'd have said that the springs and dampers just describe the coupling between the masses ... you have three masses for three linear velocities and one angular velocity ... you can track velocities of lots of other points too ... i.e. the velocities along the lengths of the springs would all be different ... but they won't all count for the purposes of this question.

 

[dla]

Hi Simon,

Thanks for replying. Just wondering where is the angular velocity located? My professor said the velocity between K1 and D1 is different than the velocity at the masses J1 and J2 and similarly the velocity between K_2 and the combination of D_2 and K_3 is different than masses J2 and J3. So would that not mean there are 5 velocities I need to consider?

 

[Simon Bridge]

I read T1 (far left) as a torque.

The velocity at the point you drew the arrow on K1 s certaily different from that for J2 or J1 - and it is probably useful for figuring the equation of motion.

Notice that J2 and J3 are connected by a single spring - while J2 and J1 are only indirectly connected through D1?

Granted D2 is connected to the middle of the spring... but the velocity of that point depends on the velocities of J2 and J3 directly so I can see why it could be ignored.

If you like - include it in your analysis and see what happens.

 

[dla]

I read T1 (far left) as a torque.

The velocity at the point you drew the arrow on K1 s certaily different from that for J2 or J1 - and it is probably useful for figuring the equation of motion.

Notice that J2 and J3 are connected by a single spring - while J2 and J1 are only indirectly connected through D1?

Granted D2 is connected to the middle of the spring... but the velocity of that point depends on the velocities of J2 and J3 directly so I can see why it could be ignored.

If you like - include it in your analysis and see what happens.

Is that single spring between J2 and J3 you mentioned, the spring of K2+K3?

 

[Simon Bridge]

That's right - the two springs would be treated as just the one with a combined K ... the wrinkle is where the damper is attached.

You could divide any of the other springs into equivalent coupled spring systems - and then track the velocity of the join. The trick is figuring which ones are important. If in doubt, include it - it will either vanish in the math or it won't.

 

[dla]

Okay got it, thank you for all your help!