Sizing of a damping - spring - mass system

AI Thread Summary
To size a damping-spring-mass system for a mass on a rod rotating 60 degrees in 120 seconds, the user has established a differential equation representing the system dynamics. The equation includes terms for inertia, damping, and spring forces. The solution for a critically damped system is provided, with a focus on determining the damping coefficient and spring constant. The discussion emphasizes the need for specific calculations to achieve the desired rotational motion within the specified time frame. Further clarification or visual aids, such as an image, may enhance understanding of the problem.
miou@mitsou
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Hello All,

I have come across a problem, which has troubled me for some time now. What needs to be done is the following:

A mass on a rod 0.6m (mass less) has a mass of 1 kgr attached at the end of it. The rod needs to be rotated 60 degrees, within t=120 sec (see image). What I would like to do is size a rotational spring (located at the pivot point) and a damping system, such that it that will damp the spring force. Thus the rotation happens within the specified amount of time.

I have written the generic differential equation of the system:

IΘ"+CΘ'+KΘ=0

and for a critical damped system for t=0, Θ=0 I have the solution:

Θ(t)=A*t*exp(-bt)

where A is a constant, and b is the damping coefficient.

My question is how can I continue, such that I can size the damping coefficient and the spring constant ?

CmBZ8TG
https://imgur.com/CmBZ8TG
CmBZ8TG
 
Last edited:
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You mention an image attachment. Could you please edit your post and attach it?

Thanks
 
done...
 
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