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• # Equations of motion spring vibration

Discussion in 'Calculations' started by goldtooth, Nov 15, 2013.

1. ### goldtoothMember

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I will need further advice but to start, does anybody know if a clock spring (torsional system) within equation of motion can have rotation and linear characteristics?

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3. ### ErichWell-Known Member

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By itself, torsion only. The rest of your mechanism has to be constrained to give the motion you want. The spring just provides the force.

4. ### goldtoothMember

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Thanks Erich. My system has contraints so that its rigid to permit rotation only (i,e the clock springs have ground points in X and Y). My next question. If i attach a lever (which has linear springs attached) to my previous system (a shaft with rotation only via clock springs) what co-ordinates can i use for the whole system? Theta? Ive got a system which has both linear and rotational springs, but is rigid to move in rotation only. I no if it can move in rotation only then it has to be theta, but im finding it hard to picture in my head the equation of motion for moments of both sets of springs.

5. ### ErichWell-Known Member

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Go back to first principles. Draw a Free body diagram. Sum the moments around the axis of rotation and set that equal to I*alpha. Express Alpha as second derivative of theta. express spring forces as functions of theta. That should result in a differential equation that describes the motion. Solution of this equation is left as an exercise for the reader.

6. ### goldtoothMember

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Thanks Erich

7. ### goldtoothMember

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Thanks for your time. Ive now got through to my differential equation with second dev of theata times mass inertia etc. Cheers. But, to get my equation i was confused at the start, I want sure if i have to split the two types of spring equations i.e equation for the lever and equation for the shaft whilst using the same Inertia and alpha? My guess is that i will have just one equation because everything is attached and i have only 1 disc, 1 mass (shaft and lever are not included for mass). For me its clear using one spring system, but joining the two has had me thinking. I will need to eventually plug this into a matrix to find the determinent, which it looks like a 1x1 matrix since it has only 1 DOF. Any thoughts on this?

Last edited: Nov 17, 2013
8. ### ErichWell-Known Member

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yes, one equation with one DOF. The spring force term will not be a simple Kx term because there are two springs with different ks etc. I cannot be any more helpful because I do not have a picture of the details of your system in mind.

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